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

共 50 条

[41] On the structure of orthosymmetric bilinear operators on vector lattices
A. G. Kusraev
Doklady Mathematics, 2006, 73 : 331 - 333
[42] b-property of sublattices in vector lattices
Gorokhova, Svetlana
Alpay, Safak
TURKISH JOURNAL OF MATHEMATICS, 2021, 45 (04) : 1555 - 1563
[43] On some vector lattices of operators and their finite elements
Hahn, Norbert
Hahn, Siegfried
Weber, Martin R.
POSITIVITY, 2009, 13 (01) : 145 - 163
[44] Canonical extensions of bounded archimedean vector lattices
Bezhanishvili, Guram
Morandi, Patrick J.
Olberding, Bruce
ALGEBRA UNIVERSALIS, 2018, 79 (01)
[45] Homogeneous orthogonally additive polynomials on vector lattices
Kusraeva, Z. A.
MATHEMATICAL NOTES, 2012, 91 (5-6) : 657 - 662
[46] Homogeneous orthogonally additive polynomials on vector lattices
Z. A. Kusraeva
Mathematical Notes, 2012, 91 : 657 - 662
[47] Canonical extensions of bounded archimedean vector lattices
Guram Bezhanishvili
Patrick J. Morandi
Bruce Olberding
Algebra universalis, 2018, 79
[48] On extensions of some nonlinear maps in vector lattices
Abasov, Nariman
Pliev, Marat
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 455 (01) : 516 - 527
[49] uτ-convergence in locally solid vector lattices
Dabboorasad, Y. A.
Emelyanov, E. Y.
Marabeh, M. A. A.
POSITIVITY, 2018, 22 (04) : 1065 - 1080
[50] Orthogonally additive operators on complex vector lattices
Pliev, Marat
Sukochev, Fedor
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2025, 541 (02)

← 1 2 3 4 5 →