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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The characteristic function of a complex symmetric contraction


Authors: Nicolas Chevrot, Emmanuel Fricain and Dan Timotin
Journal: Proc. Amer. Math. Soc. 135 (2007), 2877-2886
MSC (2000): Primary 47A45, 47B15
Published electronically: May 8, 2007
MathSciNet review: 2317964
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Abstract: It is shown that a contraction on a Hilbert space is complex symmetric if and only if the values of its characteristic function are all symmetric with respect to a fixed conjugation. Applications are given to the description of complex symmetric contractions with defect indices equal to 2.


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Additional Information

Nicolas Chevrot
Affiliation: Institut Camille Jordan, UFR de Mathématiques, Université Claude Bernard Lyon I, 69622 Villeurbanne Cedex, France
Email: chevrot@math.univ-lyon1.fr

Emmanuel Fricain
Affiliation: Institut Camille Jordan, UFR de Mathématiques, Université Claude Bernard Lyon I, 69622 Villeurbanne Cedex, France
Email: fricain@math.univ-lyon1.fr

Dan Timotin
Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Bucharest 014700, Romania
Email: Dan.Timotin@imar.ro

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08803-X
PII: S 0002-9939(07)08803-X
Keywords: Complex symmetric operator, contraction, characteristic function
Received by editor(s): April 8, 2006
Received by editor(s) in revised form: May 28, 2006
Published electronically: May 8, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society