On -Complex Symmetric Operators II

Abstract

In this paper, we study the structure of defined by the following:Delta(1)(T) In particular, we prove that if is even, then is complex symmetric with the conjugation , and if is odd, then is skew complex symmetric with the conjugation . Moreover, we investigate the conditions for ()-complex symmetric operators to be Delta(1)(T)-complex symmetric operators and characterize the spectrum of Delta(1)(T) Finally, we show that if is Hermitian or is -hyponormal, then implies Delta(1)(T) = 0