Integral Equations and Operator Theory

, Volume 59, Issue 4, pp 585–590

Remarks on the Structure of Complex Symmetric Operators

Article

DOI: 10.1007/s00020-007-1528-7

Cite this article as:
Gilbreath, T.M. & Wogen, W.R. Integr. equ. oper. theory (2007) 59: 585. doi:10.1007/s00020-007-1528-7

Abstract.

A conjugation C is antilinear isometric involution on a complex Hilbert space \({\mathcal{H}}\) , and \(T \in {\mathcal{B}}({\mathcal{H}})\) is called complex symmetric if T* = CTC for some conjugation C. We use multiplicity theory to describe all conjugations commuting with a fixed positive operator. We expand upon a result of Garcia and Putinar to provide a factorization of complex symmetric operators which is based on the polar decomposition.

Keywords.

Complex symmetric operator factorization conjugation 

Copyright information

© Birkhaueser 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA