C∗-algebra of angular Toeplitz operators on Bergman spaces over the upper half-plane

Kevin Esmeral, Egor A. Maximenko

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.
Original languageAmerican English
Pages (from-to)151-162
Number of pages134
JournalCommunications in Mathematical Analysis
StatePublished - 1 Jan 2014

Fingerprint

Bergman Space
Toeplitz Operator
Half-plane
Algebra
C*-algebra
Mathematical operators
Uniformly continuous
Real Line
Isomorphic
Metric
Chemical analysis

Cite this

@article{ad2749b440bc449496bf17239cee6d59,
title = "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.",
author = "Kevin Esmeral and Maximenko, {Egor A.}",
year = "2014",
month = "1",
day = "1",
language = "American English",
pages = "151--162",
journal = "Communications in Mathematical Analysis",
issn = "1938-9787",
publisher = "Mathematical Research Publishers",

}

C∗-algebra of angular Toeplitz operators on Bergman spaces over the upper half-plane. / Esmeral, Kevin; Maximenko, Egor A.

In: Communications in Mathematical Analysis, 01.01.2014, p. 151-162.

Research output: Contribution to journalArticle

TY - JOUR

T1 - C∗-algebra of angular Toeplitz operators on Bergman spaces over the upper half-plane

AU - Esmeral, Kevin

AU - Maximenko, Egor A.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84919638450&origin=inward

UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=84919638450&origin=inward

M3 - Article

SP - 151

EP - 162

JO - Communications in Mathematical Analysis

JF - Communications in Mathematical Analysis

SN - 1938-9787

ER -