Complex symmetric operators and applications

Garcia, Stephan; Putinar, Mihai

doi:10.1090/S0002-9947-05-03742-6

Complex symmetric operators and applications
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by Stephan Ramon Garcia and Mihai Putinar PDF

Trans. Amer. Math. Soc. 358 (2006), 1285-1315 Request permission

Abstract:

We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, self-adjoint extensions of symmetric operators, rank-one unitary perturbations of the compressed shift, Darlington synthesis and matrix-valued inner functions, and free bounded analytic interpolation in the disk.

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