VECTOR LATTICES IN SYNAPTIC ALGEBRAS

被引：4

作者：

Foulis, David J. ^{[1
]}

Jencova, Anna ^{[2
]}

Pulmannova, Sylvia ^{[2
]}

机构：

[1] Univ Massachusetts, Dept Math & Stat, 1 Sutton Court, Amherst, MA 01002 USA

[2] Slovak Acad Sci, Math Inst, Stefanikova 49, Bratislava 81473, Slovakia

来源：

MATHEMATICA SLOVACA | 2017年 / 67卷 / 06期

关键词：

synaptic algebra; vector lattice; effect algebra; generalized supremum and infimum; commutative; monotone square-root property; PROJECTIONS; MV;

D O I：

10.1515/ms-2017-0066

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2017 Mathematical Institute Slovak Academy of Sciences

引用

页码：1509 / 1524

页数：16

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