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Generalized Hankel operators on the Fock space

✍ Scribed by Georg Schneider; Kristan A. Schneider

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
171 KB
Volume
282
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In this paper we study generalized Hankel operators ofthe form : β„±^2^(|z |^2^) β†’ L^2^(|z |^2^). Here, (f):= (Id–P~l~ )($ \bar z $^k^f) and P__l__ is the projection onto A~l~ ^2^(β„‚, |z |^2^):= cl(span{$ \bar z $^m^ z^n^ | m, n ∈ N, m ≀ l }). The investigations in this article extend the ones in [11] and [6], where the special cases l = 0 and l = 1 are considered, respectively. The main result is that the operators are not bounded for l < k – 1. The proof relies on a combinatoric argument and a generalization to general conjugate holomorphic L^2^ symbols, generalizing arguments from [6], seems possible and is planned for future work (Β© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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