Hankel operators on generalized Bergman-Hardy spaces

Authors

  • Wolfgang Lusky
  • Bettina Rehberg

DOI:

https://doi.org/10.1285/i15900932v17p71

Keywords:

Hankel operators, Toeplitz operators, Bergman-Hardy spaces, Compact operators, Schatten class operators, Fourier series

Abstract

We study Hankel operators $Hf:H_2→ H2$ on a class of spaces $H2$ of analytic functions which includes, among many other examples, the Hardy space and the Bergman spaces obn the unit disk as well as the Fock space on $ℂ$. We derive compactness conditions for $Hf$ and describe the essential spectrum of $Hf*Hf$. Moreover we investigate Schatten class Hankel operators. The main objects of study are those Hankel operators $Hf$ which admit a sequence of vector-valued trigonometric polynomials $fj$ with $\limj \parallel Hf-H_{fj}\parallel=0$.

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Published

01-01-1997

Issue

Volume 17 (1997)

Section

Articoli

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