Toeplitz operators on arveson and dirichlet spaces

Daniel Alpay, H. Turgay Kaptanoğlu

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)1-33
Number of pages33
JournalIntegral Equations and Operator Theory
Volume58
Issue number1
DOIs
StatePublished - 1 Jan 2007

Keywords

  • Arveson space
  • Berezin transform
  • Bergman
  • Bergman metric
  • Bergman projection
  • Besov
  • Carleson measure
  • Dirichlet
  • Hardy
  • M-isometry
  • Schatten-von Neumann ideal
  • Toeplitz operator
  • Unitary equivalence
  • Weak convergence
  • Weighted shift

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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