Bessel fusion multipliers
type: Item
instance of: scholarly article
title: Bessel fusion multipliers
zbMATH Open document ID: 1158.42014
author: M. Laura Arias
author: Miriam Pacheco
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-10-22T00:00:00Z
full work available at URL: http://hdl.handle.net/11336/19483
review text: Let \(H\) be a separable Hilbert space. A sequence \((\psi_k)\) in \(H\) is called a Bessel sequence if there exists a positive constant \(B\) for which \[ \sum\limits_{k=1}^\infty |\langle \xi, \psi_k \rangle |^2\leq B ||\xi ||^2 \] for all \(\xi \in H\). Given two Bessel sequence \((\phi_k)\) and \((\psi_k)\) in \(H_1\) and \(H_2\) and a fixed sequence \(m=(m_k) \in\ell^\infty\), the following rescaling operator is defined \[ M_m(\psi_k)(\phi_k) (\xi)=\sum\limits_{k=1}^\infty m_k \langle \xi, \phi_k \rangle \psi_k. \] This operator is called the Bessel multiplier. The authors study properties of such multipliers when \(m\in \ell^p\). A more general concept of Bessel fusion multiplier is introduced and investigated for \(m\in \ell^p\).
reviewed by: Boris Rubin
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 46C99
Mathematics Subject Classification ID: 42B99
zbMATH DE Number: 5355958
zbMATH Keywords: Bessel multiplier
zbMATH Keywords: Bessel fusion sequence
zbMATH Keywords: Bessel fusion multiplier
MaRDI profile type: Publication
OpenAlex ID: W1998068631
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DOI: 10.1016/J.JMAA.2008.07.056
description: scientific article; zbMATH DE number 5355958