Transactions of the American Mathematical Society

Author(s): Stephan Ramon Garcia; Mihai Putinar
Journal: Trans. Amer. Math. Soc. 358 (2006), 1285-1315.
MSC (2000): Primary 30D55, 47A15
Posted: May 26, 2005
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 30D55, 47A15

Stephan Ramon Garcia
Affiliation: Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106-3080
Email: garcias@math.ucsb.edu

Mihai Putinar
Affiliation: Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106-3080
Email: mputinar@math.ucsb.edu

DOI: 10.1090/S0002-9947-05-03742-6
PII: S 0002-9947(05)03742-6
Keywords: Complex symmetric operators, interpolation, self-adjoint extension, Takagi factorization, shift operators, inner functions, Darlington synthesis, Clark perturbations, Jordan operators, Volterra operators
Received by editor(s): February 21, 2004
Received by editor(s) in revised form: May 10, 2004
Posted: May 26, 2005
Additional Notes: The second author was supported in part by NSF Grant DMS \#0100367.
Copyright of article: Copyright 2005, American Mathematical Society

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