A note on Schatten-class membership of Hankel operators with antiholomorphic symbols on generalized Fock-spaces
✍ Scribed by Georg Schneider
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 97 KB
- Volume
- 282
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
In this paper we investigate Hankel operators with anti‐holomorphic L^2^‐symbols on generalized Fock spaces A~m~^2^ in one complex dimension. The investigation of the mentioned operators was started in [4] and [3]. Here, we show that a Hankel operator with anti‐holomorphic L^2^‐symbol is in the Schatten‐class S~p~ if and only if the symbol is a polynomial with degree N satisfying 2__N__ < m and p > . The result has been proved independently before in the recent work [2], which also considers the case of several complex variables. However, in addition to providing a different proof for the result the present work shows that the methodology developed in [4] and [3] can be adopted in order to work to characterize Schatten‐class membership. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)