Research

Research interests:

I am interested in functional analysis at large. My main interests lie in the theory operator algebras. More precisely, I deal with analytic (or probabilistic) questions about L^p-spaces associated with von Neumann algebras (usually of type III). From time to time I like to take a look at the theory of operator spaces and its interplay with classical theory of Banach spaces.

Papers:

1. Amalgamated direct sums of operator spaces, Bulletin of the London Mathematical Society 48 (2016), no. 1, 155-162 (available here).
2. q-Araki-Woods algebras: extension of second quantisation and Haagerup approximation property, Proceedings of the American Mathematical Society 145 (2017), no. 12, 5287-5298 (available here).
3. Complete metric approximation property for q-Araki-Woods algebras (with S. Avsec and M. Brannan), Journal of Functional Analysis 274 (2018), no. 2, 544-572 (available here).
4. Spectral theory of Fourier--Stieltjes algebras (with P. Ohrysko), Journal of Mathematical Analysis and Applications 473 (2019), no. 1, 174-200 (available here).
5. On MASAs in q-deformed von Neumann algebras (with M. Caspers and A. Skalski), Pacific Journal of Mathematics 302 (2019), no. 1, 1-21. (available here).
6. Bigalois Extensions and the Graph Isomorphism Game (with M. Brannan, A. Chirvasitu, K. Eifler, S. Harris, V. Paulsen, and X. Su), Communications in Mathematics Physics (2019) (available here ).
7. Inversion problem in measure and Fourier-Stieltjes algebras (with P. Ohrysko), Journal of Functional Analysis 278 (2020), no. 5, 19 pp. (available here).
8. L₂-cohomology, derivations and quantum Markov semi-groups on q-Gaussian algebras (with M. Caspers and Y. Isono), to appear in International Mathematics Research Notices (available here).
9. A simple proof of the complete metric approximation property for q-Gaussian algebras, to appear in Colloquium Mathematicum (available here).