Non-commutative Arens algebras and their derivations

被引：21

作者：

Albeverio, S. ^{[2
]}

Ayupov, Sh. A. ^{[1
]}

Kudaybergenov, K. K. ^{[1
]}

机构：

[1] Uzbek Acad Sci, Math Inst, Tashkent 700143, Uzbekistan

[2] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2007年 / 253卷 / 01期

关键词：

von neumann algebras; non-commutative integration; Arens algebras; derivations; spatial derivations; inner derivations; operator algebras; quantum statistical mechanics;

D O I：

10.1016/j.jfa.2007.04.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a von Neumann algebra M with a faithful normal semi-finite trace tau, we consider the non-commutative Arens algebra L-omega(M, tau) = boolean AND(p >= 1) L-p(M, tau) and the related algebras L-2(omega)(M, tau) = boolean AND(p >= 2) L-p(M, tau) and M + L-2(omega)(M, tau) which are proved to be complete metrizable locally convex *-algebras. The main purpose of the present paper is to prove that any derivation of the algebra M + L-2(omega)(M, tau) is inner and all derivations of the algebras L-omega(M, tau) and L-2(omega)(M, tau) are spatial and implemented by elements of M + L-2(omega)(M, tau). In particular we obtain that if the trace tau is finite then any derivation on the non-commutative Arens algebra L-omega(M, tau) is inner. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：287 / 302

页数：16