SKEW COMPLEX SYMMETRIC OPERATORS AND WEYL TYPE THEOREMS

Abstract

An operator T is an element of L(H) is said to be skew complex symmetric if there exists a conjugation C on H such that T = -CT*C. In this paper, we study properties of skew complex symmetric operators including spectral connections, Fredholmness, and subspace-hypercyclicity between skew complex symmetric operators and their adjoints. Moreover, we consider Weyl type theorems and Browder type theorems for skew complex symmetric operators.