Complex symmetry & weighted composition operators on fock spaces

Abstract

The main results of the thesis lie at the intersection of three areas: dynamical systems, complex symmetric operators, and weighted composition operators. We introduce two new concepts: weighted composition conjugations in operator theory, and complex symmetric C 0 -semigroups (C 0 -groups) in dynamical systems. Notations ixA bounded linear operator T is compact on a Banach space X if for every bounded sequence (x n ), (T x n ) has a convergent subsequence. In the case that X is reflexive, this definition is equivalent to the fact that the operator T maps weakly convergent sequences into norm convergent sequences (see [22, p. 200]).