Mathematics Research
I am broadly interested in the theory of operator algebras; in particular, the foundational/structural aspects of the theory of von Neumann algebras. The study of `rings of operators' was developed (by Murray and von Neumann) to describe a framework for the mathematical foundations of quantum mechanics. In recent work, I have explored the algebraic structure of the set of affiliated operators for von Neumann algebras. As a work in progress, I am trying to learn the ropes of quantum information theory, which naturally has led me towards CP-maps and the study of classical convex geometry as well as noncommutative versions such as C*-convexity.
"...... we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury." - Irving Kaplansky, on the late Paul Halmos.Publications/Preprints
| 13. | (with R Shekhawat) A stronger form of Yamamoto's theorem II – Spectral operators | [arXiv:2410.16318] |
| 12. | (with I Ghosh) Algebraic aspects and functoriality of the set of affiliated operators, International Mathematics Research Notices, Volume 2024, Issue 21 (2024), 13525–13562. | [DOI:10.1093/imrn/rnae203] [arXiv:2311.16170] |
| 11. | A stronger form of Yamamoto's theorem on singular values, Linear Algebra and its Applications, Volume 679 (2023), 231–245. | [DOI:10.1016/j.laa.2023.08.026] [arXiv:2303.01252] |
| 10. | (with B V Rajarama Bhat and P Shankar) On the products of symmetries in von Neumann algebras, J. Operator Theory 92, Issue 2, (2024), 579–596. | [arXiv:2204.00009] |
| 9. | A conceptual approach towards understanding matrix commutators, The Mathematics Student, Volume 91 (2022), Nos. 1-2. | [Online copy] [Local copy] |
| 8. | A framework for rank identities - With a view towards operator algebras, J. Operator Theory 89, Issue 2 (Spring 2023), 477–520. | [arXiv:1801.08072] |
| 7. | The Douglas lemma for von Neumann algebras and some applications, Adv. Oper. Theory 6, 47 (2021). | [DOI:10.1007/s43036-021-00143-4] [arXiv:1707.04378] |
| 6. | On Murray-von Neumann algebras - I: topological, order-theoretic and analytical aspects, Banach J. Math. Anal. 15, 45 (2021). | [DOI:10.1007/s43037-021-00129-7] [arXiv:1911.01978] |
| 5. | Matrix algebras over algebras of unbounded operators, Banach J. Math. Anal. 14 (2020), 1055–1079. | [DOI:10.1007/s43037-019-00052-y] [arXiv:1812.06872] |
| 4. | A constructive proof of the derivation theorem, The Mathematics Student, Volume 88 (2019), Nos. 3-4, 119–124. | [Online copy] [Local copy] |
| 3. | Jensen's inequality in finite subdiagonal algebras, Bull. Lond. Math. Soc. 50 (2018), no. 6, 1102–1112. | [DOI:10.1112/blms.12208] [arXiv:1807.11652] |
| 2. | (with M. Gaál) On a class of determinant preserving maps for finite von Neumann algebras, J. Math. Anal. Appl. 464 (2018), no. 1, 317–327. | [DOI:10.1016/j.jmaa.2018.04.006] [arXiv:1711.08786] |
| 1. | The Hadamard determinant inequality - Extensions to operators on a Hilbert space, J. Funct. Anal. 274 (2018), no. 10, 2978–3002. | [DOI:10.1016/j.jfa.2017.10.009] [arXiv:1704.05421] |
Preprints
Notes
| S. Nayak; An operator inequality for range projections | [arXiv:1804.09683] |