Designation
Associate Professor
Joining Date
Expiry of Tenure
Research Area
Functional Analysis
Education
- Doctor of Philosophy : University of Delhi, Delhi, India in 1998.
- Master Degree : University of Delhi, Delhi, India in 1990.
Research Interest
Order structure in normed spaces and operator spaces (matricially normed spaces);
Theory of operator ideals (Geometry of Banach Spaces).
Publications
- Matrix norms in matrix ordered spaces, Anil K. Karn and R. Vasudevan; Glasnik Mathematici, 32(1)(1997) 87-97.
- Approximate matrix order unit spaces, Anil K. Karn and R. Vasudevan; Yokohama Math. J., 44(1997) 73-91.
- Matrix duality for matrix ordered spaces, Anil K. Karn and R. Vasudevan; Yokohama Math. J., 45(1998) 1-18.
- Characterizations of matricially Riesz normed spaces, Anil K. Karnand R. Vasudevan; Yokohama Math. J., 47(2000) 143-153.
- Compact operators whose adjoints factor through subspaces of lp , D. P. Sinha and Anil K. Karn; Studia Mathematica, 150(1) (2002) 17-33.
- Order units in a C*-algebra, Anil K. Karn; Pros. Indian Acad. Sci.(Math. Sci.), 113(1)(2003) 65-69.
- Adjoining an order unit to a matrix ordered space, Anil K. Karn;Positivity, 9(2) (2005) 207-223.
- Direct limit of matrix ordered spaces, J. V. Ramani, Anil K. Karn and Sunil Yadav; Glasnik Matematicki., 40(2) (2005) 303-312
- Direct limit of matricially Riesz normed spaces, J. V. Ramani, Anil K. Karn and Sunil Yadav; Commentationes Mathematicae Universitatis Carolinae, 47(1) (2006) 55-67.
- Corrigendum to “Adjoining an order unit to a matrix ordered space”, Anil K. Karn; Positivity, 11(2) (2007) 369-374.
- Direct limit of matrix order unit spaces, J. V. Ramani, Anil K.Karn and Sunil Yadav; Colloquium Mathematicum, 113(2) (2008), 175-184.
- Compact operators which factor through subspaces of $\ell_p$ , D. P. Sinha and Anil K. Karn; Math. Nachr., 281(3) (2008), 412-423.
- A p- theory of ordered normed spaces, Anil K. karn; Positivity, 14(3), (2010), 441–458.
- Order embedding of a matrix ordered space, Anil K. Karn; Bulletin Aust. Math. Soc., 84(1) (2011), 10–18.
- Orthogonality in sequence spaces and its bearing on ordered Banach spaces, Anil K. Karn; Positivity, 18(2) (2014), 223-234.
- An operator summability in Banach spaces, Anil K. Karn and D. P. Sinha; Glassgow Math. J., 56(2) (2014), 427-437.
- Orthogonality in a C*-algebra, Anil K. Karn; Positivity, 20(3) (2016), 607- 620. (https://rdcu.be/6pJl)
- Compact factorization of operators with λ-compact adjoints, Antara Bhar and Anil Kumar Karn; Glassgow Math. J., 60(2018), no. 1, 123-134.
- Algebraic orthogonality and commuting projections in operator algebras, Anil Kumar Karn; Acta Sci. Math. (Szeged), 84(1-2) (2018), 323-353.
- $M$-ideals and split faces of the quasi state space of a non-unital ordered Banach space, Anindya Ghatak and Anil Kumar Karn; Positivity, 23(2) (2019), 413-429. (https://rdcu.be/7RZx).
- Contractive linear preservers of absolutely compatible pairs between C$^*$-algebras, Nabin K. Jana, Anil K. Karn and Antonio M. Peralta; Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas (RCSM), 113(3) (2019) 2731-2741. (https://rdcu.be/bo9Ln)
- $CM$-ideals and $L^{1}$-matricial split faces, Anindya Ghatak and Anil K. Karn; Acta Sci. Math. (Szeged), 85(3-4) (2019), 659-679.
- Absolutely compatible pairs in a von Neumann algebra, N. K. Jana, A. K. Karn and A. M. Peralta, Electronic Journal of Linear Algebra, 35 (2019), 599-618.
- Quantization of $A_{0}(K)$-Spaces, Anindya Ghatak and Anil Kumar Karn; Operator and Matrices, 14(2) (2020), 381-399.
- Absolutely compatible pairs in a von Neumann algebra-II, Anil K.umar Karn; Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas (RCSM), 114(3), July (2020). Article 153, 7pages. (https://rdcu.be/b4Tw6)
- Isometries of Absolute order unit spaces, Anil Kumar Karn and Amit Kumar; Positivity, 24(5) (2020), 1263-1277.
- Partial isometries in an absolute order unit space, Anil Kumar Karn and Amit Kumar; Banach Journal of Mathematical Analysis, 15(1) (2021), 1-26. (https://rdcu.be/cbdDL)
- Orthogonality: an antidote to Kadison's anti-lattice theorem, Anil Kumar Karn; Positivity and its Applications, (Positivity X, 8-12 July 2019), Pretoria, South Africa, (2021), 217-227.
- $K_0$-group of absolute Matrix order unit spaces, Anil Kumar Karn and Amit Kumar; Karn, Adv. Oper. Theory, 40(2) (2021) 27 pages. (Published online on March 17, 2021), (https://rdcu.be/cgX4P).
- A generalization of spin factors, Anil Kumar Karn; Acta. Sci. Math. (Szeged)), 87 (2021), 551-569.
- Absolute compatibility and Poincare sphere, Anil Kumar Karn, Annals of Functional Analysis Published online on April 12, 2022), 13 pages; doi:10.1001/s43034-022-00186-5, (https://arxiv.org/abs/2110.13108)
Preprints
- Centre of a compact convex set, Anil Kumar Karn, 16 pages, (Communicated for publication.); https://arxiv.org/abs/2201.07671
- Compactness and an approximation property related to an operator ideal, Anil K. Karn and D. P. Sinha; (Preprint). (https://arxiv.org/abs/1207.1947)
- Dual of a normed F-bimodule, Anil K. Karn; (Preprint).
Project/Thesis Guidance
- Anindya Ghatak, completed in 2019,
- Amit Kumar, completed in 2020.
Sponsored Projects
- SERB sponsered Mathematical Research Impact Centric Support (MATRICS) project entitled "Absolute matrix order unit spaces: an order theoretic generalization of C*-algebras" of Rs. 6,60,000 for three years starting from 2020. Project reference no. MTR/2020/000017.