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Journal of Operator Theory

Volume 72, Issue 2, Fall 2014  pp. 529-547.

A canonical decomposition of complex symmetric operators

Authors:  Kunyu Guo (1) and Sen Zhu (2)
Author institution: (1) School of Mathematical Sciences, Fudan University,\break Shanghai, 200433, P.R. China
(2) Department of Mathematics, Jilin University, Changchun, 130012, P.R. China

Summary:  An operator $T$ on a complex Hilbert space $\mathcal{H}$ is said to be complex symmetric if there exists a conjugate-linear, isometric involution $C:\mathcal{H}\rightarrow\mathcal{H}$ so that $CTC=T^*$. In this paper, we obtain a canonical decomposition of complex symmetric operators. This result decomposes general complex symmetric operators into direct sums of three kinds of elementary ones.

Keywords:  complex symmetric operator, transpose, UET operator, canonical decomposition, irreducible operator, completely reducible operator, Toeplitz operator

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