Remarks on Complex Symmetric Operators

Abstract

An operator is said to be complex symmetric if there exists a conjugation C on such that . In this paper, we study the spectral radius algebras for complex symmetric operators. In particular, we prove that if A is a complex symmetric operator, then the spectral radius algebra associated with A has a nontrivial invariant subspace under some conditions. Finally, we give some relations between and (defined below) when A is complex symmetric.