Algebras of Toeplitz Operators on the n-Dimensional Unit Ball

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Authors

  • Wolfram Bauer
  • Raffael Hagger
  • Nikolai Vasilevski

Research Organisations

External Research Organisations

  • Center for Research and Advanced Studies of the National Polytechnic Institute
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Details

Original languageEnglish
Pages (from-to)493-524
Number of pages32
JournalComplex Analysis and Operator Theory
Volume13
Issue number2
Early online date25 Aug 2018
Publication statusPublished - 13 Mar 2019

Abstract

We study C ∗ -algebras generated by Toeplitz operators acting on the standard weighted Bergman space Aλ2(Bn) over the unit ball B n in C n . The symbols f ac of generating operators are assumed to be of a certain product type, see (1.1). By choosing a and c in different function algebras S a and S c over lower dimensional unit balls B ℓ and B n - ℓ , respectively, and by assuming the invariance of a∈ S a under some torus action we obtain C ∗ -algebras T λ (S a , S c ) of whose structural properties can be described. In the case of k-quasi-radial functions S a and bounded uniformly continuous or vanishing oscillation symbols S c we describe the structure of elements from the algebra T λ (S a , S c ) , derive a list of irreducible representations of T λ (S a , S c ) , and prove completeness of this list in some cases. Some of these representations originate from a “quantization effect”, induced by the representation of Aλ2(Bn) as the direct sum of Bergman spaces over a lower dimensional unit ball with growing weight parameter. As an application we derive the essential spectrum and index formulas for matrix-valued operators.

Keywords

    Irreducible representations, Operator C -algebra, Weighted Bergman spaces

ASJC Scopus subject areas

Cite this

Algebras of Toeplitz Operators on the n-Dimensional Unit Ball. / Bauer, Wolfram; Hagger, Raffael; Vasilevski, Nikolai.
In: Complex Analysis and Operator Theory, Vol. 13, No. 2, 13.03.2019, p. 493-524.

Research output: Contribution to journal › Article › Research › peer review

Bauer W, Hagger R, Vasilevski N. Algebras of Toeplitz Operators on the n-Dimensional Unit Ball. Complex Analysis and Operator Theory. 2019 Mar 13;13(2):493-524. Epub 2018 Aug 25. doi: 10.48550/arXiv.1808.10372, 10.1007/s11785-018-0837-y
Bauer, Wolfram ; Hagger, Raffael ; Vasilevski, Nikolai. / Algebras of Toeplitz Operators on the n-Dimensional Unit Ball. In: Complex Analysis and Operator Theory. 2019 ; Vol. 13, No. 2. pp. 493-524.
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