Toeplitz operators on generalized Bergman-Hardy spaces
DOI:
https://doi.org/10.7146/math.scand.a-14316Abstract
We study the Toeplitz operators Tf:H2→H2, for f∈L∞, 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 f∈L∞ with limj‖Tf−Tfj‖=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 f∈X, whenever Tf is compact, and characterize these functions in a simple and straightforward way. Finally, we determine those f∈L∞ where Tf is a Hilbert-Schmidt operator.Downloads
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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