PROPERTIES OF COMPLEX SYMMETRIC OPERATORS

Abstract

An operator T is an element of L(H) is said to be complex symmetric if there exists a conjugation C on H such that T = CT*C. In this paper, we prove that every complex symmetric operator is biquasitriangular. Also, we show that if a complex symmetric operator T is weakly hypercyclic, then both T and T* have the single-valued extension property and that if T is a complex symmetric operator which has the property (delta), then Weyl's theorem holds for f (T) and f (T)* where f is any analytic function in a neighborhood of sigma(T). Finally, we establish equivalence relations among Weyl type theorems for complex symmetric operators.