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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
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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:

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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