Complex symmetric operators and their Weyl type theorems (The research of geometric structures in quantum information based on Operator Theory and related topics)

Abstract

We study a necessary and sufficient condition for complex symmetric operator matrices to satisfy a-Weyl s theorem. Moreover, we also give the conditions for such operator matrices to satisfy generalized a-Weyl s theorem and generalized a-Browder s theorem, respectively. As some applications, we provide various examples of such operator matrices which satisfy Weyl type theorems.