Alexey Popov

It a classical open problem in Operator Theory whether every bounded linear operator T on a Hilbert space H has a non-trivial invariant subspace (that is, a subspace Y of H such that TY is contained in Y; nontrivial means not {0} and not H). This is...

An algebra is a vector space with a well-defined multiplication. An operator algebra is an algebra of operators acting on a Hilbert space, typically assumed closed in the norm topology. An easy example of an operator algebra is the algebra M_n(C) of...

In this talk we will outline a large class of problems in Analysis (in particular, Matrix Analysis) called the Preserver Problems and then concentrate on a specific preserver problem: study the structure of isometries defined on the algebra A of...