Toeplitz operators on Arveson and Dirichlet spaces

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2007-05-01

Author

Alpay, Daniel
Kaptanoglu, H. Turgay

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We define Toeplitz operators on all Dirichlet spaces on the unit ball of C-N 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.

Subject Keywords

Algebra and Number Theory, Analysis

URI

https://hdl.handle.net/11511/65057

Journal

INTEGRAL EQUATIONS AND OPERATOR THEORY

DOI

https://doi.org/10.1007/s00020-007-1493-1

Collections

Department of Mathematics, Article

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Citation Formats

D. Alpay and H. T. Kaptanoglu, “Toeplitz operators on Arveson and Dirichlet spaces,” INTEGRAL EQUATIONS AND OPERATOR THEORY, pp. 1–33, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65057.