Complex symmetric operators and applications |
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Authors: | Stephan Ramon Garcia Mihai Putinar |
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Institution: | Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106-3080 ; Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106-3080 |
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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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Keywords: | Complex symmetric operators interpolation self-adjoint extension Takagi factorization shift operators inner functions Darlington synthesis Clark perturbations Jordan operators Volterra operators |
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