, Volume 59, Issue 4, pp 585-590
Date: 18 Oct 2007

Remarks on the Structure of Complex Symmetric Operators

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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.

This paper is based in part on the first author’s Master’s Project.