Multiplication operators on Hilbert spaces of analytic functions
type: Item
instance of: scholarly article
title: Multiplication operators on Hilbert spaces of analytic functions
zbMATH Open document ID: 1061.47028
published in: Archiv der Mathematik
publication date: 2005-01-20T00:00:00Z
review text: Let \(H\) be a Hilbert space of functions analytic on a plane domain \(\Omega\). The \(\mathbb C\)-hull of \(\Omega\) is denoted by \(\Omega^*\) and denote by \(\Omega_1\) the component of \(\Omega^*\) containing \(\Omega\). A complex-valued function \(\varphi\) on \(\Omega\) for which \(\varphi f\in H\) for every \(f\in H\) is called a multiplier of \(H\) and the collection of all these multipliers is denoted by \(M(H)\). Assume that each point of \(\Omega\) is a bounded point evaluation and that \(H\) contains the constant functions and \(z\in M(H)\). The author proves that if \(\{e_{\lambda}:\lambda\in\Omega\}\) is norm bounded and \(H^{\infty}(\Omega_1)\subset M(H)\), then \(M_z\) is reflexive.
reviewed by: Hasi Wulan
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 47A25
zbMATH DE Number: 2130598
zbMATH Keywords: Hilbert space
zbMATH Keywords: evaluation
zbMATH Keywords: reflexivity
author: Bahmann Yousefi
MaRDI profile type: Publication
full work available at URL: s00013-004-1040-0
OpenAlex ID: W1972751912
DOI: 10.1007/S00013-004-1040-0
description: scientific article; zbMATH DE number 2130598