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 lim where (f_j) is a sequence of vector-valued trigonometric polynomials whose coefficients are radial functions. For these T_f we obtain explicit descriptions of their essential spectra. Moreover, we show that f \in X, whenever T_f is compact, and characterize these functions in a simple and straightforward way. Finally, we determine those f \in L_\infty where T_f 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