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The characteristic function of a complex symmetric contraction
Author(s):
Nicolas
Chevrot;
Emmanuel
Fricain;
Dan
Timotin
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2877-2886.
MSC (2000):
Primary 47A45, 47B15
Posted:
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.
References:
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- 1.
- Gr. Arsene and A. Gheondea, Completing matrix contractions, J. Operator Theory 7 (1982), 179-189. MR 0650203 (83i:47010)
- 2.
- C. Foias and A.E. Frazho, The Commutant Lifting Approach to Interpolation Problems, Birkhäuser Verlag, Basel, 1990. MR 1120546 (92k:47033)
- 3.
- S.R. Garcia, Conjugation, the backward shift, and Toeplitz kernels, J. Operator Theory 54:2 (2005), 239-250. MR 2186351 (2006g:30055)
- 4.
- -, Conjugation and Clark operators, Contemporary Mathematics, vol. 393, Amer. Math. Soc., Providence, RI, 2006. MR 2198373
- 5.
- S.R. Garcia and M. Putinar, Complex symmetric operators and applications, Trans. Amer. Math. Soc. 358:3 (2006), 1285-1315. MR 2187654 (2006j:47036)
- 6.
- B. Sz-Nagy and C. Foias, Harmonic Analysis of Operators on Hilbert Space, North Holland, New York, 1970. MR 0275190 (43:947)
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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:
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
Posted:
May 8, 2007
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
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