Communications in Mathematical Analysis

C*-algebra of Angular Toeplitz Operators on Bergman Spaces over the Upper Half-plane

K. Esmeral and E. Maximenko

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Abstract

We consider the C*-algebra generated by Toeplitz operators acting on the Bergman space over the upper half-plane whose symbols depend only on the argument of the variable. This algebra is known to be commutative, and it is isometrically isomorphic to a certain algebra of bounded complex valued functions on the real numbers. In the paper we prove that the latter algebra consists of all bounded functions f that are very slowly oscillating on the real line in the sense that the composition of f with sinh is uniformly continuous with respect to the usual metric.

Article information

Source
Commun. Math. Anal., Volume 17, Number 2 (2014), 151-162.

Dates
First available in Project Euclid: 18 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.cma/1418919761

Mathematical Reviews number (MathSciNet)
MR3292965

Zentralblatt MATH identifier
1327.30063

Subjects
Primary: 30H20: Bergman spaces, Fock spaces 46L05: General theory of $C^*$-algebras 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15] 47L80: Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)

Keywords
Toeplitz operator Bergman space invariant under dilation slowly oscillating function

Citation

Esmeral, K.; Maximenko, E. C*-algebra of Angular Toeplitz Operators on Bergman Spaces over the Upper Half-plane. Commun. Math. Anal. 17 (2014), no. 2, 151--162. https://projecteuclid.org/euclid.cma/1418919761


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