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February 2017 Similarity orbits of complex symmetric operators
Sen Zhu, Jiayin Zhao
Ann. Funct. Anal. 8(1): 63-74 (February 2017). DOI: 10.1215/20088752-3750041


An operator T on a complex Hilbert space H is said to be complex symmetric if T can be represented as a symmetric matrix relative to some orthonormal basis for H. In this article we explore the stability of complex symmetry under the condition of similarity. It is proved that the similarity orbit of an operator T is included in the class of complex symmetric operators if and only if T is an algebraic operator of degree at most 2.


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Sen Zhu. Jiayin Zhao. "Similarity orbits of complex symmetric operators." Ann. Funct. Anal. 8 (1) 63 - 74, February 2017.


Received: 3 April 2016; Accepted: 17 June 2016; Published: February 2017
First available in Project Euclid: 31 October 2016

zbMATH: 1353.47075
MathSciNet: MR3566891
Digital Object Identifier: 10.1215/20088752-3750041

Primary: 47A05 , 47B99
Secondary: 47A10 , 47A58

Keywords: complex symmetric operator , essentially normal operator , similarity , similarity orbit

Rights: Copyright © 2017 Tusi Mathematical Research Group


Vol.8 • No. 1 • February 2017
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