Toeplitz Operators on Arveson and Dirichlet Spaces |
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Authors: | Daniel Alpay H Turgay Kaptano?lu |
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Institution: | (1) Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel;(2) Department of Mathematics, Bilkent University, Ankara, 06800, Turkey |
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Abstract: | We define Toeplitz operators on all Dirichlet spaces on the unit ball of
and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive
symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman
spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting
case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of
bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate
some connections between Toeplitz and shift operators.
The research of the second author is partially supported by a Fulbright grant. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 47B35 32A37 Secondary 47B07 47B10 47B37 47B33 46E22 32A36 32A35 |
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