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Complex symmetric operators and applications


Authors: Stephan Ramon Garcia and Mihai Putinar
Journal: Trans. Amer. Math. Soc. 358 (2006), 1285-1315
MSC (2000): Primary 30D55, 47A15
Published electronically: May 26, 2005
MathSciNet review: 2187654
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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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Additional Information

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: http://dx.doi.org/10.1090/S0002-9947-05-03742-6
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
Published electronically: May 26, 2005
Additional Notes: The second author was supported in part by NSF Grant DMS #0100367.
Article copyright: © Copyright 2005 American Mathematical Society