Toeplitz operators with vertical symbols acting on the poly-Bergman spaces of the upper half-plane
type: Item
instance of: scholarly article
title: Toeplitz operators with vertical symbols acting on the poly-Bergman spaces of the upper half-plane
zbMATH Open document ID: 1343.47081
author: Armando Sánchez-Nungaray
author: Josué Ramírez-Ortega
published in: Complex Analysis and Operator Theory
publication date: 2015-11-09T00:00:00Z
review text: Recall that the \(n\)-analytic Bergman space \(\mathcal{A}^2_n(\Pi)\) on the upper half-plane \(\Pi\) is the closed subspace of \(L_2(\Pi)\) that consists of all \(n\)-analytic functions, i.e., those functions \(\varphi\) that satisfy the equation \((\partial/\partial \overline{z})^n \varphi = 0\). The authors study the \(C^*\)-algebra generated by all Toeplitz operators \(T_a\) acting on \(\mathcal{A}^2_n(\Pi)\) whose bounded measurable symbols \(a\) depend only on \(y =\mathrm{Im}\,z\) and have limit values at \(y=0\) and \(y = \infty\). They show the the above \(C^*\)-algebra is isometrically isomorphic to the algebra of all \(n\times n\) matrix-functions that are continuous on the positive real axis \(\mathbb{R}_+\) and are the scalar multiples of identity at \(y=0\) and \(y = \infty\).
Mathematics Subject Classification ID: 47L80
Mathematics Subject Classification ID: 30H99
Mathematics Subject Classification ID: 32A25
zbMATH DE Number: 6506176
zbMATH Keywords: special symbols
zbMATH Keywords: algebras of Toeplitz operators
zbMATH Keywords: poly-Bergman space
zbMATH Keywords: poly-Bergman projection
MaRDI profile type: Publication
full work available at URL: s11785-015-0469-4
OpenAlex ID: W244932629
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DOI: 10.1007/S11785-015-0469-4
description: scientific article; zbMATH DE number 6506176