Lattice of tripotents in a \(\text{JBW}^*\)-triple
type: Item
instance of: scholarly article
title: Lattice of tripotents in a \(\text{JBW}^*\)-triple
zbMATH Open document ID: 0841.03033
DOI: 10.1007/BF00676247
published in: International Journal of Theoretical Physics
publication date: 1996-07-16T00:00:00Z
review text: This paper is motivated by interest in `non-associative non-commutative' probabilities over nonclassical propositional systems represented by orthomodular lattices. It is suggested that the appropriate structures of interest here will not be spaces with binary multiplication, but instead triple spaces. In particular the authors are concerned with tripotents (analogous to idempotents in binary systems), and claim to show here that the collection of tripotents in the complex Banach spaces known as JBW* algebras, when supplemented by a largest element, forms a complete lattice. In addition they purport to show that subsystems of this lattice which are associative, are equivalently described either by `norm-closed faces of the generalised normal state space' or by principal ideals in the JBW* triple. The paper is a technical exposition, and the results are not explicitly used to explore the wider issues of nonclassical propositional and probability structure which motivate it.
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 06C15
zbMATH DE Number: 844062
zbMATH Keywords: orthomodular lattices
zbMATH Keywords: triple spaces
zbMATH Keywords: tripotents
zbMATH Keywords: complex Banach spaces
zbMATH Keywords: JBW* algebras
zbMATH Keywords: state space
author: C. M. Edwards
author: Gottfried T. Rüttimann
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00676247
OpenAlex ID: W2001578226
description: scientific article; zbMATH DE number 844062