## Communications in Mathematical Analysis

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

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

#### 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