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Grant 19-07129Y     1.1.2019 - 31.12.2021
Grantor: Czech Science Foundation

Linear-analysis techniques in operator algebras and vice versa


The theory of normed spaces and their operators is at the core of the linear analysis. The idea of employing algebras of operators acting on infinite-dimensional spaces originated in quantum physics and was further successfully integrated with the theory of unitary representations of locally compact groups. An operator algebra, which is also a normed space, carries intrinsically a much richer structure and therefore operator algebras are not usually viewed from the perspective of linear analysis. Nevertheless, the transfer of ideas from Banach spaces can be very fruitful as illustrated by the notion of nuclearity that was recognised as an approximation property with respect to a certain class of finite-rank operators. On the other hand, operator Ktheory
was almost unknown in Banach space theory until it was spectacularly applied in the seminal work of Gowers and Maurey. Consequently, there is tremendous potential in transferring ideas between these two areas. The very aim of the project is a closer reconciliation of these two theories by interchanging ideas between them.

 Main investigator:

Kania Tomasz

 Participating institutions:

Institute of Mathematics, Czech Academy of Sciences