Toeplitz operators on generalized Bergman-Hardy spaces

Authors

  • Wolfgang Lusky

DOI:

https://doi.org/10.7146/math.scand.a-14316

Abstract

We study the Toeplitz operators Tf:H2H2, for fL, on a class of spaces H2 which in- cludes, among many other examples, the Hardy and Bergman spaces as well as the Fock space. We investigate the space X of those elements fL with limjTfTfj=0 where (fj) is a sequence of vector-valued trigonometric polynomials whose coefficients are radial functions. For these Tf we obtain explicit descriptions of their essential spectra. Moreover, we show that fX, whenever Tf is compact, and characterize these functions in a simple and straightforward way. Finally, we determine those fL where Tf is a Hilbert-Schmidt operator.

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Published

2001-03-01

How to Cite

Lusky, W. (2001). Toeplitz operators on generalized Bergman-Hardy spaces. MATHEMATICA SCANDINAVICA, 88(1), 96–110. https://doi.org/10.7146/math.scand.a-14316

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Articles