A Banach principle for \(L^ \infty\)
type: Item
instance of: scholarly article
title: A Banach principle for \(L^ \infty\)
zbMATH Open document ID: 0878.46020
author: Roger Jones
author: Alexandra Ionescu Tulcea
published in: Advances in Mathematics
publication date: 1996-08-11T00:00:00Z
review text: In the context of the spaces \(L^p\) with \(1\leq p<\infty\), the classical Banach principle relates the a.e. convergence of a sequence of operators and the finiteness of the corresponding maximal function. The authors formulate a version of this principle for \(L^\infty\); it relates the a.e. convergence of a sequence of operators and the continuity of the maximal function at zero on the ball of \(L^\infty\) if this ball is endowed with the topology of convergence in measure. Some applications are given.
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 47B60
zbMATH DE Number: 915231
zbMATH Keywords: a.e. convergence of a sequence of operators
zbMATH Keywords: maximal function
zbMATH Keywords: topology of convergence in measure
reviewed by: S. V. Kislyakov
MaRDI profile type: Publication
full work available at URL: aima.1996.0035
OpenAlex ID: W2040424986
DOI: 10.1006/AIMA.1996.0035
description: scientific article; zbMATH DE number 915231