Synaptic algebras

被引：18
|
作者：
Foulis, David J. [1 ]
机构：
[1] Univ Massachusetts, Amherst, MA 01003 USA
来源：
MATHEMATICA SLOVACA | 2010年 / 60卷 / 05期
关键词：
spectral order-unit normed space; special Jordan algebra; convex effect algebra; orthomodular lattice; generalized Hermitian algebra; projections; square roots; carriers; absolute value; polar decoposition; quadratic mapping; Sasaki mapping; invertible element; regular element; simple element; spectral resolution; spectrum;
D O I：
10.2478/s12175-010-0037-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A synaptic algebra is both a special Jordan algebra and a spectral order-unit normed space satisfying certain natural conditions suggested by the partially ordered Jordan algebra of bounded Hermitian operators on a Hilbert space. The adjective "synaptic", borrowed from biology, is meant to suggest that such an algebra coherently "ties together" the notions of a Jordan algebra, a spectral order-unit normed space, a convex effect algebra, and an orthomodular lattice.
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页码：631 / 654
页数：24
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