Hilbert-Schmidt Hankel operators on the Segal-Bargmann space

Author:
Wolfram Bauer

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2989-2996

MSC (2000):
Primary 47B35

DOI:
https://doi.org/10.1090/S0002-9939-04-07264-8

Published electronically:
June 2, 2004

MathSciNet review:
2063120

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper considers Hankel operators on the Segal-Bargmann space of holomorphic functions on that are square integrable with respect to the Gaussian measure. It is shown that in the case of a bounded symbol the Hankel operator is of the Hilbert-Schmidt class if and only if is Hilbert-Schmidt. In the case where the symbol is square integrable with respect to the Lebesgue measure it is known that the Hilbert-Schmidt norms of the Hankel operators and coincide. But, in general, if we deal with bounded symbols, only the inequality can be proved. The results have a close connection with the well-known fact that for bounded symbols the compactness of implies the compactness of .

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Additional Information

**Wolfram Bauer**

Affiliation:
Department of Mathematics, State University of New York, Buffalo, New York 14260

Address at time of publication:
Johannes Gutenberg Universität Mainz, Fachbereich Mathematik und Informatik, Staudinger Weg 9, 55128 Mainz, Germany

Email:
BauerWolfram@web.de

DOI:
https://doi.org/10.1090/S0002-9939-04-07264-8

Received by editor(s):
July 10, 2002

Received by editor(s) in revised form:
February 15, 2003

Published electronically:
June 2, 2004

Additional Notes:
This work was supported by a fellowship of the \itshape“Deutscher akademischer Austauschdienst” (DAAD)

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2004
American Mathematical Society