Weyl Type Theorems for Complex Symmetric Operator Matrices

Abstract

In this paper,

we study Weyl type theorems for complex symmetric operator matrices.

In particular, we give a necessary and sufficient condition for complex symmetric operator matrices to satisfy $a$-Weyl's theorem.

Moreover, we also

provide the conditions for such operator matrices to satisfy generalized $a$-Weyl's theorem and generalized $a$-Browder's theorem, respectively. As some applications, we give various examples of such operator matrices which satisfy Weyl type theorems.