NISER

• Doctor of Philosophy : University of Delhi, Delhi, India in 1998.
• Master Degree : University of Delhi, Delhi, India in 1990.

Functional Analysis

1. On the geometry of order unit spaces, Anil Kumar Karn, Advances in Operator Theory 9, 28 (2024)(March 24, 2024) 18 pages.(https://doi.org/10.1007/s43036-024-00327-8)  
2. Centre of a compact convex set, Anil Kumar Karn; Banach Journal of Mathematical Analysis, 16(4) (2022), Article 68, 19 pages. (https://doi.org/10.1007/s43037-022-00222-5)
3. Absolute compatibility and Poincare sphere, Anil Kumar Karn, Annals of Functional Analysis, Ann. Funct. Anal. 13, 39 (2022), 13 pages. (https://doi.org/10.1007/s43034-022-00186-5)
4. A generalization of spin factors, Anil Kumar Karn; Acta. Sci. Math. (Szeged)), 87 (2021), 551-569.
5. $K_0$-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).
6. Orthogonality: an antidote to Kadison's anti-lattice theorem, Anil Kumar Karn; Positivity and its Applications, Trends in Mathematics, Birkhauser, Switzerland, (2021), 217-227.
7. 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)
8. Isometries of Absolute order unit spaces, Anil Kumar Karn and Amit Kumar; Positivity, 24(5) (2020), 1263-1277.
9. 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)
10. Quantization of $A_{0}(K)$-Spaces, Anindya Ghatak and Anil Kumar Karn; Operator and Matrices, 14(2) (2020), 381-399.
11. 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.
12. $CM$-ideals and $L^{1}$-matricial split faces, Anindya Ghatak and Anil K. Karn; Acta Sci. Math. (Szeged), 85(3-4) (2019), 659-679.
13. 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)
14. $M$-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).
15. Algebraic orthogonality and commuting projections in operator algebras, Anil Kumar Karn; Acta Sci. Math. (Szeged), 84(1-2) (2018), 323-353.
16. Compact factorization of operators with  λ-compact  adjoints, Antara Bhar and Anil Kumar Karn; Glassgow Math. J., 60(2018), no. 1, 123-134.
17. Orthogonality in a C*-algebra, Anil K. Karn; Positivity, 20(3) (2016), 607- 620. (https://rdcu.be/6pJl)
18. An operator summability in Banach spaces, Anil K. Karn and D. P. Sinha; Glassgow Math. J., 56(2) (2014), 427-437.
19. Orthogonality in sequence spaces and its bearing on ordered Banach spaces, Anil K. Karn; Positivity, 18(2) (2014), 223-234.
20. Order embedding of a matrix ordered space, Anil K. Karn; Bulletin Aust. Math. Soc., 84(1) (2011), 10–18.
21. A $p$- theory of ordered normed spaces, Anil K. karn; Positivity, 14(3), (2010), 441–458.
22. Compact operators which factor through subspaces of $\ell_p$ , D. P. Sinha and Anil K. Karn; Math. Nachr., 281(3) (2008), 412-423.
23. Direct limit of matrix order unit spaces, J. V. Ramani, Anil K.Karn and Sunil Yadav; Colloquium Mathematicum, 113(2) (2008), 175-184.
24. Corrigendum to “Adjoining an order unit to a matrix ordered space”, Anil K. Karn; Positivity, 11(2) (2007) 369-374.
25. 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.
26. Direct limit of matrix ordered spaces, J. V. Ramani, Anil K. Karn and Sunil Yadav; Glasnik Matematicki., 40(2) (2005) 303-312.
27. Adjoining an order unit to a matrix ordered space, Anil K. Karn;Positivity, 9(2) (2005) 207-223.
28. Order units in a C*-algebra, Anil K. Karn; Pros. Indian Acad. Sci.(Math. Sci.), 113(1)(2003) 65-69.
29. Compact operators whose adjoints factor through subspaces of lp , D. P. Sinha and Anil K. Karn; Studia Mathematica, 150(1) (2002) 17-33.
30. Characterizations of matricially Riesz normed spaces, Anil K. Karnand R. Vasudevan; Yokohama Math. J., 47(2000) 143-153.
31. Matrix duality for matrix ordered spaces, Anil K. Karn and R. Vasudevan; Yokohama Math. J., 45(1998) 1-18.
32. Matrix norms in matrix ordered spaces, Anil K. Karn and R. Vasudevan; Glasnik Mathematici, 32(1)(1997) 87-97.
33. Approximate matrix order unit spaces, Anil K. Karn and R. Vasudevan; Yokohama Math. J., 44(1997) 73-91.

Preprints:

1. A generalization of Lipschitz mappings, Anil Kumar Karn and Arindam Mandal, (priprint). 
2. Order unit property and orthogonality, Anil Kumar Karn, (priprint). (https://arxiv.org/abs/2410.07623)
3. Normed linear spaces which are isometric to order unit spaces, Anil Kumar Karn, (priprint). (https://arxiv.org/abs/2306.06549)
4. Compactness and an approximation property related to an operator ideal, Anil K. Karn and D. P. Sinha; (Preprint). (https://arxiv.org/abs/1207.1947)

Order structure in normed spaces and operator spaces (matricially normed spaces)
Theory of operator ideals (Geometry of Banach Spaces).