Vector lattices in synaptic algebras-Reference-Cited by-同舟云学术

Vector lattices in synaptic algebras

Published:2017-11-01 Issue:6 Volume:67 Page:1509-1524
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Foulis David J.¹,Jenčová Anna²,Pulmannová Sylvia²

Affiliation:

1. Department of Mathematics and Statistics , University of Massachusetts , 1 Sutton Court , Amherst , MA 01002 , USA

2. Mathematical Institute , Slovak Academy of Sciences , Štefánikova 49 814 73 , Bratislava , Slovakia

Abstract

Abstract A synaptic algebra A is a generalization of the self-adjoint part of a von Neumann algebra. We study a linear subspace V of A in regard to the question of when V is a vector lattice. Our main theorem states that if V contains the identity element of A and is closed under the formation of both the absolute value and the carrier of its elements, then V is a vector lattice if and only if the elements of V commute pairwise.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0066/pdf

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