On Banach lattice algebras of type 1
type: Item
instance of: scholarly article
title: On Banach lattice algebras of type 1
zbMATH Open document ID: 1039.46039
DOI: 10.1007/BF02390821
author: Egon Scheffold
published in: Arkiv för Matematik
publication date: 2004-03-15T00:00:00Z
review text: It is known that a finite-dimensional real Banach algebra lattice with unit, such that every positive element is regular, is norm and lattice isomorphic to \(\mathbb R\), and it is unknown whether the result holds in the infinite-dimensional case. The aim of this paper is to prove its validity for Banach algebra lattices of type 1. A Banach algebra lattice \(A\) with unit \(e\) is called of type 1 if \(a(e+a)^{-1} \geq 0\) for every \(a\geq 0\).
Mathematics Subject Classification ID: 46H99
Mathematics Subject Classification ID: 46B42
zbMATH DE Number: 2057355
zbMATH Keywords: Banach algebra lattice
reviewed by: Stefan Cobzaş
MaRDI profile type: Publication
cites work: Q3215824
cites work: Q4049667
cites work: Über komplexe Banachverbandsalgebren
cites work: Banachverbandsalgebren mit einer natürlichen Wedderburn-Zerlegung
cites work: On spectral properties of positive operators
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description: scientific article; zbMATH DE number 2057355