On \(m\)-complex symmetric operators
type: Item
instance of: scholarly article
title: On \(m\)-complex symmetric operators
zbMATH Open document ID: 1394.47031
author: Muneo Chō
author: Eungil Ko
author: Jieun Lee
published in: Mediterranean Journal of Mathematics
publication date: 2016-08-31T00:00:00Z
review text: An antilinear operator \(C\) acting on a complex separable Hilbert space \(H\) is said to be a conjugation if \(C^2=I\) and \(\langle Cx,Cy\rangle=\langle y,x \rangle\) for all \(x,y\in H\). A bounded linear operator \(T\) on \(H\) is a \(C\)-complex symmetric operator if \(T^*=CTC\). Motivated by the Helton class operators, the authors introduce the class of \(m\)-complex symmetric operator as a generalization of the class of complex symmetric operators: \(T\) is said to be \(m\)-complex symmetric if \[ \sum_{k=0}^m(-1)^{m-k}\begin{pmatrix} m\\k\end{pmatrix} T^{*k}CT^{m-k}C=0 \] for some positive integer \(m\). Then they study the spectral properties of \(m\)-complex symmetric operators. Among other things, they prove that, if \(T\) is \(m\)-complex symmetric with conjugation \(C\), then \(T^n\) is \(m\)-complex symmetric with the same conjugation for any \(n\in\mathbb{N}\). Some local spectral properties for \(m\)-complex symmetric operators are also investigated.
reviewed by: H. Zguitti
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 47A11
zbMATH DE Number: 6620740
zbMATH Keywords: \(m\)-complex symmetric operator
zbMATH Keywords: decomposable operators, single valued extension property
MaRDI profile type: Publication
full work available at URL: s00009-015-0597-0
OpenAlex ID: W798838750
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DOI: 10.1007/S00009-015-0597-0
description: scientific article; zbMATH DE number 6620740