On the sublinear functional associated to a family of invariant means
type: Item
instance of: scholarly article
title: On the sublinear functional associated to a family of invariant means
zbMATH Open document ID: 0598.47031
DOI: 10.1007/BF01168616
author: B. George
published in: Manuscripta Mathematica
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155130
review text: Conditions are given under which explicit analytic expressions can be obtained for the fundamental sublinear functional \(\rho_ K(x)=\sup \{\mu (x):\) \(\mu\in K\}\) associated to a family of means \(K=[G]\cap J\), where \(x\in \ell^{\infty}\), G is a subset of means on \(\ell^{\infty}\) invariant with respect to a semigroup of operators G and J is a saturated set of means on \(\ell^{\infty}\). Under such conditions it is possible to assure that \(K\neq \emptyset.\) A relation is also obtained between \(\rho_ K\) and \(\rho_ J\) which allows to give \(\rho_ K\) in terms of \(\rho_ J\) when \(\rho_ J\) is known and different equivalent expressions for \(\rho_ K\) if the family J changes and K is fixed. From this several examples are given.
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 46A45
zbMATH DE Number: 3964769
zbMATH Keywords: generalized limits of Banach
zbMATH Keywords: invariant means
zbMATH Keywords: almost convergent sequences
zbMATH Keywords: saturated set
zbMATH Keywords: explicit analytic expressions
zbMATH Keywords: fundamental sublinear functional
zbMATH Keywords: semigroup of operators
zbMATH Keywords: saturated set of means
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3964769