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
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
收藏
页码:287 / 302
页数:16
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