Article ID Journal Published Year Pages File Type
4616632 Journal of Mathematical Analysis and Applications 2013 13 Pages PDF
Abstract

An operator T∈L(H)T∈L(H) is said to be complex symmetric if there exists a conjugation JJ on HH such that T=JT∗JT=JT∗J. In this paper, we find several kinds of complex symmetric operator matrices and examine decomposability of such complex symmetric operator matrices and their applications. In particular, we consider the operator matrix of the form T=(AB0JA∗J) where JJ is a conjugation on HH. We show that if AA is complex symmetric, then TT is decomposable if and only if AA is. Furthermore, we provide some conditions so that aa-Weyl’s theorem holds for the operator matrix TT.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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