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.
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This paper is based in part on the first author’s Master’s Project.
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Gilbreath, T.M., Wogen, W.R. Remarks on the Structure of Complex Symmetric Operators. Integr. equ. oper. theory 59, 585–590 (2007). https://doi.org/10.1007/s00020-007-1528-7
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DOI: https://doi.org/10.1007/s00020-007-1528-7