On characterization of integrable sesquilinear forms
We give necessary and sufficient condition for a sesquilinear form to be integrable with respect to a faithful normal state on a von Neumann algebra.
math.OA↗
arXiv subjects
Oleg E. Tikhonov
Publications and source records attributed to Oleg E. Tikhonov.
The uniqueness of the solution to inverse interpolation problems
We prove that an arbitrary Banach couple is uniquely determined by the collection of intermediate spaces that are interpolation spaces for the operators of rank one. From this we deduce a confirmation to the conjecture by Yu. A. Brudnyi and N.Ya. Kruglyak that a Banach couple is uniquely determined by the collection of all its interpolation spaces. Some relevant problems are also analized.
math.FA↗