Approximation and symbolic calculus for Toeplitz algebras on the Bergman space

Daniel Suárez

    Research output: Contribution to journalArticleResearchpeer-review

    19 Citations (Scopus)

    Abstract

    If f ∈ L∞ (double-struck D sign) let Tf be the Toeplitz operator on the Bergman space La2 of the unit disk double-struck D sign. For a C*-algebra A ⊂ L∞(double-struck D sign) let script I sign(A) denote the closed operator algebra generated by {Tf : f ∈ A}. We characterize its commutator ideal c(A) and the quotient script I sign(A)/c(A) for a wide class of algebras A. Also, for n ≥ 0 integer, we define the n-Berezin transform BnS of a bounded operator 5, and prove that if f ∈ L∞(double-struck D sign) and fn = BnTf then Tfn→Tf.
    Original languageEnglish
    Pages (from-to)563-610
    JournalRevista Matematica Iberoamericana
    Volume20
    Issue number2
    DOIs
    Publication statusPublished - 1 Jan 2004

    Keywords

    • Bergman space
    • Commutator ideal and abelianization
    • Toeplitz operator

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