Functional Analysis : Operator Theory

• Ph.D. Mathematics , 2009 , University of Delhi
• M.Phil. Mathematics , 1989 , University of Delhi
• Certificate in French , 1988 , University of Delhi
• M.Sc. Mathematics , 1986 , HansRaj College,University of Delhi

Started as Ad-Hoc Lecturer in Department of Mathematics, Hansraj College, University of Delhi in 1987.Continuing since then and currently working as Professor.

Subjects Taught:

• Undergraduates

1. B. A./ B. Sc. (Hons.) Mathematics

1. Metric Spaces (Semester, FYUP and CBCS Mode)
2. Complex Analysis (Semester, FYUP and CBCS Mode)
3. Bio Mathematics (Semester mode)
4. Discrete mathematics (Annual Mode and Semester Mode)
5. Analysis – IV (Riemann Integration) (Annual Mode)
6. Analysis – I (Annual Mode)
7. Calculus (Annual Mode)
8. Algebra – I (Semester Mode)
9. Real Analysis (Semester Mode)

1. B. Com. (Hons.)

1.     Business Mathematics (Annual Mode)

1. B. Sc. (H) (Chemistry)

1.     Calculus (Semester mode)
2.     Coordinate Geometry and Algebra (Annual Mode)

1. B.Sc. (Physical sciences)

1.     Real Analysis (Semester mode)
2.     Calculus (Annual Mode)

1. B.Sc.(H) Physics
   1. PHHT-413, Paper-15: Mathematics-II (Sem. Mode)
2. Postgraduates

M.A/ M.Sc. Mathematics

1.     Topology-I ((Department of Mathematics, University of Delhi, 2018-19, Sem. II)
2.     Differential Geometry (Department of Mathematics, University of Delhi, 2017-18, Sem. IV)

IT usage and Software: Basics of MS word, MS Excel, MS PPT, Maxima, Mathematica and LaTeX & HTML

PhD

Reading Course: Math16-30 ‘Banach Algebra Techniques in Operator Theory to Ph.D. scholars in the Department of Mathematics, University of Delhi in 2016-17.

1. M.Phil.: Completed  1. Harshita Shekhar (Department of Mathematics, Univ. of Delhi): Topic: Classes of Operators satisfying Weyl Type Theorems
2. PhD Guidance: (i) SonuRam,: Degree Awarded; Thesis Title: Algebraic and Spectral Properties of (m,n)-Paranormal and (m,n)*-Paranormal Operators; ii) Sarita Kumari,: Thesis submitted; Title: Browder Spectral Theory over the Complex and Quaternionic Hilbert Spaces; Ongoing--->(iii) Ramkishan (iv)Asphak Ahmed (v) Pradeep Singh

1. College Bursar :2020-2023 (November)
2. Presiding Officer: Internal Complaints Committee of the College( 2019-20, 2020-21)
3. Member: IQAC (2015-till date)
4. Convenor: Admission: University Ward Quota (2020-21)
5. Convenor: College Moderation Committee (2020-21)
6. Nodal Officer: NIRF (2018-19, 2019-20)
7. Coordinator: NAAC(2015-17)
8. Faculty Development Centre, Hansraj College under PMMMNMTT (MHRD): Director(2018-19)
9. Convenor: Library(2016-17, 2017-18)
10. Convenor: Grievance Redressal Committee (2016-17)
11. Convenor: Student Union Advisory Committee (2016-17)
12. Superintendent: Examinations, Hansraj College  (2000, 2002, 2010)
13. Secretary: Staff Council, Hansraj College (1999-2000)
14. Secretary: Hansraj College Alumni Association (2015-18)
15. Convenor: Admissions (Sciences) (2014-15)
16. Teacher-in-Charge: Department of Mathematics  ( 1995-96, 2008-09 and 2015-16)
17. Convenor: Environment Awareness Committee "Haritima" ( 2009-2010, 2010-2011 and 2013-2014)
18. Convenor: Publications Committee ( 2013-2014)
19. Convenor: Hansraj@Antardhwani (Best Paractices) ( 2013-14, 2014-15)
20. Member: Executive Committee  : Hansraj College Alumni Association ( 2012-15)
21. Treasurer: Hansraj College Alumni Association (2006-2009, 2009-2012)
22. Convenor: Society for General Awareness  (2015-16, 2016-17, 2017-18)
23. Convenor: Student Welfare Committee

1.  Ph.D. Thesis: A study of Weighted Weyl Spectra of Operators

2. M.Phil. Dissertation: A study of Commutants of Analytic Toeplitz Operators

1. Aankalan, The Annual Journal of Department of Mathematics, Hansraj College, Volume 1, 2020 ; Volume2, 2021; Volume 3, 2022: Head , Advisory Editorial Board
2. Chapter in an Edited Book: A generalization of class W of operators, Proceedings of IMBIC( 2018), Vol.7, ISBN 978-81-925832-6-6, pp.157-164.
3. Finite Mathematics for Business, Economics, Life Science and Social Sciences (Barnett, Ziegler and Byleen), published by Pearson (2015): ISBN-9781292062297,
4. Questions in Analysis for B.Sc.(Hons.) Mathematics in 2008-2009: ILLL (DU)Website (ISSN 2349-154X).

1. Sonu ram and Preeti Dharmarha; Totally (m,n)- paranormal operators; Gulf Journal of Mathematics, Vol 15, Issue 1 ( Aug. 2023) 57-66; ISSN: 2309-4966
2. Sonu Ram and Preeti Dharmarha;  Riesz idempotent, spectral mapping theorem and Weyl's theorem for (m,n)*-paranormal operators; Random Operators and Stochastic Equations, July 2023.
3. Preeti Dharmarha and Sarita Kumari: Properties of Fredholm, Weyl and Jeribi essential S-spectra in a right quaternionic Hilbert Space: Reviews in Mathematical Physics, Vol. 35 (July, 2023).
4. Preeti Dharmarha and Sarita Kumari: A Note On The Properties of Pseudo-Weighted Browder Spectrum: Bulletin of Korean Mathematical Society, 60(Jan. 2023), No.1 pg nos.123-135, pISSN: 1015-8634 / eISSN: 2234-3016
5. Preeti Dharmarha and Sarita Kumari: On Weighted Browder Spectrum; Bulletin of Korean Mathematical Society, Jan. 2022, pg nos.1-13
6. Preeti Dharmarha: गणित अध्ययन: हिंदी माध्यम की चुनौतियाँ; Samsamyik Srijan, 2320-5733
7. Preeti Dharmarha and Sonuram: Spectral mapping theorem and Weyl's theorem for (m, n)-paranormal operators; Filomat 35:10 (2021), 3293–3302
8. Preeti Dharmarha and Sonuram: A note on (m,n)-paranormal operators: Electronic Journal of Mathematical Analysis and Applications, ISSN 2090-729X/  Vol. 9(1) January, 2021-Pg. 274-283
9.  Preeti Dharmarha and Sonuram:A note on (m,n)*-paranormal operators: Novi Sad Journal of Mathematics;  Novi Sad J. Math. Vol. 51, No. 2, 2021

10.  Preeti Dharmarha and Sonuram:(m,n)-paranormal operators and (m, n)*-paranormal operators: Communications of the Korean Mathematical Society 35(2020), No.1, pp.151-159, pISSN: 1225-1763/eISSN: 2234

11. S C Arora and Preeti Dharmarha: On left weighted spectrum: Vigyan Garima Sindhu, CSTT Vol.108 (Jan-March, 2019) ISSN: 2320-7736, pp.262-267

12. Preeti Dharmarha and Savita Rani: V-Shaped Toeplitz Operators : International Journal Of Pure and Applied Mathematics, ISSN: 1311-8080, (2017), Vol. 114.

13. Preeti Dharmarha: On Left Weighted Weyl's Theorem: Bulletin of the Allahabad Mathematical Society Vol. 23, Part 2, 285-292, ISSN: 0971-0493

14. Preeti Dharmarha: Weighted Weyl Spectrum: Ganita, Vol. 58, No. 1 (2007), 67-74, ISSN:0046-5402

15. S C Arora and Preeti Dharmarha: On Joint Weighted Spectrum: Bull. Cal. Math. Soc., 99, (5) (2007), 539-546, ISSN: 008-0659

16. S C Arora and Preeti Dharmarha: Operators satisfying Re(sigma(alpha(T)))= Sigma(alpha(Re(T)): International Journal of Pure and Applied Mathematics, Bulgaria, Vol. 34, No. 2 (2007), 197-202, ISSN:1311-8080

17. S C Arora and Preeti Dharmarha: Weighted Weyl spectrum II: Bulletin of Korean Mathematical Society 43 (2006), No. 4, 715-722, ISSN: 1015-8634

Organization of a Conference/ Workshop/Seminars

National Level:

1.    National Seminar on Draft New Education Policy:2019

NIRF Related: 

2.    Quest for Quality: Ranking and Accreditation (Online), May 23, 2020.

ICC related:

1. Role of ICC and Prevention, Prohibition and Redressal of Sexual Harassment at Workplace (Online)\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\, May22, 2020.
2. Organized one-day workshop on Prevention of Sexual Harassment at Workplace (for non-teaching staff of the college), June 2019.

Library related:

1.     5. Four Day Training Programme on KOHA (ILMS) for Library Staff in 2016.

Subject (Mathematics) related:

National Level:

1.    National Seminar on Draft New Education Policy:2019

NIRF Related: 

2.    Quest for Quality: Ranking and Accreditation (Online), May 23, 2020.

ICC related:

1. Role of ICC and Prevention, Prohibition and Redressal of Sexual Harassment at Workplace (Online)\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\, May22, 2020.
2. Organized one-day workshop on Prevention of Sexual Harassment at Workplace (for non-teaching staff of the college), June 2019.

Library related:

1.     5. Four Day Training Programme on KOHA (ILMS) for Library Staff in 2016.

Subject (Mathematics) related:

6.    Shanti Narayan Mathematics Conclave: Launch of first edition of "Aankalan" – Department of Mathematics, Hansraj College,; Keynote speaker: Dr. S. R. Arora(Ex.Principal Hansraj College), Guest of Honour: Mr.  Sanjiv Narayan,Feb.27, 2020.

7.    Seminar: Foreign education and admission process, Department of Mathematics, Hansraj College; Speaker: Dr. Anusha Srivastava- Columbia University (USA) , November 9, 2019.

8.    Hands on Session cum Workshop: Applications of Linear algebra, Department of Mathematics, Hansraj College; Speaker: Prof. Shobha Bagai,(Dean: Admissions, Prof.CIC,DU) , September 23, 2019.

1. As a member of Finance Committee in International Conference on Operator Theory and Related Areas, Department of Mathematics, Delhi University
2. National Conference on Advances in Mathematics organized by NBHM at Hansraj College, University of Delhi; 2014.
3. Organized the following seminars in the department:
4. Seminar on Acturial Sciences
5. Seminar titled “Mathematics in Indus Valley Civilization” by Prof. Dinesh Singh
6. Inter College Seminar on “Management for Mathematics students” by Dr. N. K. Oberoi, 2008
7. Seminar on Logic by Prof. S. C. Arora
8. Inter College Seminar titled “Mathematics and Politics” by Dr. Sudeshna Basu from George Washington University, USA; 2013 on World Ozone day
9. Inter College Seminar titled “Symmetry on Mathematics” by Dr. Kalyan Bidhan Sinha from Statistics and Mathematics Unit, Delhi Centre, Indian Statistical Institute, 2014.

Environment related:

Organized the following for the Environment Awareness Committee of the College:

1. A talk by Magsaysay Award Winner Water Man of India, Dr. Rajendra Singh.
2. A seminar on e-waste Management.
3. A seminar on paper recycling.
4. Panellist, Inter College discussion on “Ozone depletion & its effects on day to day life” sponsored by Millennium India Education Foundation, held at Hansraj College, Delhi University, 2013 on World Ozone day.
5. Debate on “Science is for the Scientist, Lets’ not confuse” judged by Finance Officer of Delhi University and Prof. Subhadra Channa, Department of Anthropology, Delhi University.

Session Chaired at a conference:  International Conference on Mathematical Analysis and its Applications (ICMAA-2019) organized by Department of Mathematics, South Asian University, New Delhi, Dec.2019

Papers presented in Conferences/ Workshops/ Symposium:

1. Title: Ancient Indian Mathematics and the World: 5th Annual National Conference, Rashtriya Samaj Vigyan Parishad (RSVP)
   Social Sciences in India's Knowledge Tradition, October 15-17, 2022
2. Title: V-shaped Toeplitz operators; International Conference on Analysis and Its Applications; Nepal Mathematical Society, April 11, 2021
3. Title: A generalization of class W of operators: (International) MSAST, with workshop on Mathematical and Statistical Applications in Life Sciences and Engineering, Dec.21-23, 2018
4. Title: Left Spectrum of weight; National Workshop on Modelling, Optimization and Data Analytics; IIT Roorkee, Roorkee, October, 2018
5. Title: Metric Spaces and related topics; DU Pre- Entrance Summer School-2018, June-2018
6. Title: On Left Weighted Spectrum: International Conference on Operator Theory and Related Areas (ICOTRA)(2008)
7. Title: Riemann Integration: Refresher Course in Mathematics (Maths-14), (1998)

Resource Person/Invited Resource Person/InvitedTalks at Conference/ Workshops/ Seminars:

1. Metric Spaces: (National) Virtual Workshop on Collating Mathematics Resources for Teachers in Higher Education, October 7, 2020
2. Left Weighted Weyl Spectrum and Left Weighted Weyl Theorem: International Conference on Mathematical Analysis and its Applications (ICMAA-2019),Department of Mathematics, South Asian University, New Delhi, ( December 14,2019)
3. Weighted Essential Spectrum and a class of operators: National Conference on Advances in Mathematical Analysis and its Applications (NCAMAA-2019), Department of Mathematics, PGDAV College, University of Delhi, New Delhi ( November 9, 2020)
4. A Generalization of Left Essential Spectrum: 21st Annual Conference of Vijnana Parishad of India Modelling, Optimization and Computing for Technological and Sustainable Development (MOCTSD-2019), Department of Mathematics, SRM institute of Science and Technology, Ghaziabad (U.P.) ( April, 2019)
5. Class Wα of Operators: National Seminar on Mathematical Modelling, Optimization and Scientific Comp, Department of Mathematics, Hindu Girls College, Sonepat in collaboration with Global Society of Mathematical and Allied Sciences ( Feb. 23, 2019)
6. Left Spectrum of weight- α: National Workshop on Modelling, Optimization and Data Analytics, IIT Roorkee, Roorkee ( Oct.15, 2018)
7. Compactness and Connectedness: DU Pre- Entrance Summer School-2018, University of Delhi,Delhi(June 7, 2018)
8. Completeness, Total boundedness and Separability: DU Pre- Entrance Summer School-2018, University of Delhi,Delhi(June 6, 2018)
9. Metric Spaces: DU Pre- Entrance Summer School-2018, University of Delhi,Delhi(June 5, 2018)
10. More about Weighted Weyl Spectrum: Fourth International Conference of Applied Mathematics and Computers (FICAMC), Plodiv, Bulgaria (2007)

Conferences Attended:

1. International Conference on Mathematical Analysis and its Applications (ICMAA-  2019), Department of Mathematics, South Asian University, New Delhi, Sponsoring Agency: SAU, CSIR, SERB , Dec. 2019
2. National Conference on Advances in Mathematical Analysis and its Applications (NCAMAA-2019), Department of Mathematics, PGDAV College, University of Delhi, New Delhi, Sponsoring Agency: SERB-DST, Nov. 2019
3. 12th International Conference MSAST, Dec.21-23, 2018, with workshop on Mathematical and Statistical Applications in Life Sciences and Engineering; jointly organised by IMBIC and MAKUT, Kolkata, West Bengal
4. National Workshop on Modelling, Optimization and Data Analytics, (14-15 October 2018), IIT Roorkee, Roorkee.
5. Annual Conference of Indian Women and Mathematics, IISc., Bengaluru, 2017
6. 14th Discussion Meeting on Harmonic Analysis, Department of mathematics, University of Delhi, 2015.
7. National Conference on Advances in Mathematics sponsored by NBHM at Hansraj   College, University of Delhi; 2014.
8. National Symposium on Functional Analysis, Optimization and Their Applications (FAOTA’s), Delhi, India
9. International Conference on Operator Theory and Related Areas (ICOTRA), Delhi, India, 2008
10. Fourth International Conference of Applied Mathematics and Computers, Plodiv, Bulgaria, 2007
11. National Symposium on Recent Advances in Optimization Theory and Application (RAOTA-2006), Delhi, India  

 Workshops Attended:

1. Two Weeks (Online) Workshop on Vedic Mathematics organized by Shiksha Sanskriti Utthan Nyas, New Delhi in collaboration with Mahatma Hansraj Faculty Development Centre, Hansraj College, University of Delhi; December 2-13, 2021
2. Virtual Workshop on Collating Mathematics Resources for Teachers in Higher Education, National Institute of Educational Planning and Administration (NIEPA). October 6-7, 2020.
3. Five days’ National Webinar : Financial Mathematics: Pedagogy and Career Perspectives, Department of Mathematics, Lady Shri Ram College For Women, July 27-31, 2020.
4. Two weeks Faculty Development Program (Online): Biomathematics, Department of Mathematics, PGDAV College with Mahatma Hansraj Faculty Development Centre under PMMMNMT;Oct.15- 28, 2020.
5.  One week Faculty Development Program: Open Source Tools for Research; Teaching Learning Centre, Ramanujan College (under PMMMNMTT) (Online); June8-June 14, 2020.
6. Two weeks Faculty Development Program: Managing Online classes & Co-creating MOOCS:2.0, Teaching Learning Centre, Ramanujan College (under PMMMNMTT) (Online); May 18- June 3, 2020. 
7. One week Faculty Development Program: E-Learning, MOOCS and ICT Tools for Blended Learning, GAD Teaching Learning Centre, S.G.T.B. Khalsa College, Univ. of Delhi, Delhi; July02-July07, 2018.
8. International Workshop on Operator Spaces, Department of Mathematics, University of Delhi; 2015.
9. Workshop on Role of Technical Dictionary in Higher Education organized by Commission for Scientific and Technical Terminology, 2015.
10. National Workshop on e- Content Development for Enhancing Pedagogical Skills for Teachers in Higher Education: a complete e- content Productions Experiment at Christ University, Bangalore, organized by CEDBEC, Bangalore; Sept. 9- 11,2014.
11. Workshop on Building Mathematical Ability, organized by CPDHE (UGC-ASC); 2013
12. Workshop on Free/ open Source Software, “Maxima”, ANDC, Delhi University, 2012
13. National Workshop on “Differential Equations Computing and Modelling”, Department of Mathematics, Delhi University, 2010
14. Mathematica Workshop, South Campus, Delhi University, 2010
15. National Workshop on Analysis, 2007
16. Instructional Workshop on Fractal Geometry and Non-linear Dynamic Systems, Delhi, Delhi University, 2004
17. Windows 95, MS Word and Power Point Workshop, Computer Centre, Delhi University, 2001
18. Internet Concepts and Applications, Computer Centre, Delhi University, 1999
19. Three Weeks Professional Development Programme in Analysis (Code: Math-14), CPDHE, Delhi University, 1998
20. Three Weeks Professional Development Programme in Discrete Mathematics (Code: Math-4), CPDHE, Delhi University, 1993
21. Three Weeks Professional Development Programme on Numerical analysis & Computer Programming and Differential Equations (Code: Math-2), CPDHE, Delhi University, 1992

Awards Received:

1.  Life Time Achievement Award: In International Research Awards on Science, Technology and Management-INSO, 2022
2. Dr. Sarvepalli Radhakrishnan Best Teacher Award 2021: Centre for Professional Advancement
3. Excellence in Teaching Award by Hansraj College on successful completion of 30 years of service in 2018
4.  Appreciation Award by DAV College Managing Committee for the contribution towards first cycle of NAAC for the College in 2017 as Steering Committee Convenor (College scored 3.62 with A+)
5. Appreciation Award by Hansraj College for the contribution towards first cycle of NAAC for the College in 2017 as Steering Committee Convenor (College scored 3.62 with A+)
6. NET, JRF (1987)

Contribution to Curriculum Development:

1.  Member, Committee of Courses for Undergarduates: Faculty of Mathematical Sciences, University of Delhi (2021-23)
2. Course Convenor: Online Certificate course (SLC Course 01)- Duration:30 Hours:  Introduction to Computer Algebra System (CAS): Maxima (An Open Source Software), June 28- July 18, 2020); Student Learning Centre: Hansraj College.
3. Worked with Department of Mathematics, Delhi University as member for UG Syllabus Revision Committee under CBCS -2018
4. Worked as Committee Member for the following papers of B.Sc.(H) Maths (LOCF) in Delhi University (2018-19):

•  BMATH203: Real Analysis (B.Sc.(H) Mathematics (Sem II))
• BMATH307: Multivariate Calculus (with practicals) ( B.Sc.(H) Mathematics, Sem III)
• BMATH511: Metric Spaces (B.Sc.(H) Mathematics, Sem V)
• BMATH613: Complex Analysis (B.Sc.(H) Mathematics, Sem VI)
• DSE-2(ii): Discrete mathematics (B.Sc.(H) Mathematics, Sem V)
• DSE-3(iii): Biomathematics (B.Sc.(H) Mathematics, Sem VI)

4      Worked as  Core Committee Member-syllabus formulation for the paper ‘Discrete Mathematics’ of  B.Sc.(H) Mathematics ( FYUP) in 2013-14 

Selection Committee Membership:

1. Member, Selection Committee for DAV Colleges(outside Delhi)
2.  Member, Selection Committee for DAV Schools for PGT and TGT appointments (Delhi).

Association with Professional Bodies

1. Life Member: Indian Mathematical Society, Hyderabad 
2. Life Member: Ramanujan Mathematical Society, Chennai 
3. Life Member: Mathematics Teachers Association, TIFR, Mumbai 
4. Life Member: Vijnana Parishad of India 
5. Board Member for International Journal of Multidisciplinary Research and Modern Education, published by R&D Modern Research Publication, Perambalur, Tamilnadu, India: ISSN (online) 2454-6119
6. Honorary Member: Academic Council, Swami Vivekananda Subharti University (SVSU), Meerut: 2019-2022