Toeplitz Operators on Arveson and Dirichlet Spaces |
| |
Authors: | Daniel Alpay H. Turgay Kaptanoğlu |
| |
Affiliation: | (1) Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel;(2) Department of Mathematics, Bilkent University, Ankara, 06800, Turkey |
| |
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. |
| |
Keywords: | KeywordHeading" >Mathematics Subject Classification (2000). Primary 47B35, 32A37 Secondary 47B07, 47B10, 47B37, 47B33, 46E22, 32A36, 32A35 |
本文献已被 SpringerLink 等数据库收录! |
|