An operator (Formula presented.) is said to be complex symmetric if there exists a conjugation C on (Formula presented.) such that (Formula presented.). 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 (Formula presented.) associated with A has a nontrivial invariant subspace under some conditions. Finally, we give some relations between (Formula presented.) and (Formula presented.) (defined below) when A is complex symmetric.
Bibliographical notePublisher Copyright:
© 2015, Springer Basel.
- Complex symmetric operator
- Invariant subspace
- Spectral radius algebra