AF-Subalgebras of a C*-Algebra Generated by a Mapping

被引：2

作者：

Grigoryan, S. A. ^{[1
]}

Kuznetsova, A. Yu. ^{[2
]}

机构：

[1] Kazan State Energy Univ, Ul Krasnoselskaya 51, Kazan 420066, Russia

[2] Kazan VI Lenin State Univ, Kazan 420008, Russia

来源：

RUSSIAN MATHEMATICS | 2010年 / 54卷 / 03期

关键词：

AF-algebra; C*-algebra; partial isometry;

D O I：

10.3103/S1066369X10030102

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider a C*-subalgebra of the algebra of all bounded operators B(l(2)(X)) on theHilbert space l(2)(X) with one generating element T-phi induced by a mapping phi of a set X into itself. We prove that such a C*-algebra has an AF-subalgebra and establish commutativity conditions for the latter. We prove that a C*-algebra generated by a mapping produces a dynamic system such that the corresponding group of automorphisms is invariant on elements of the AF-subalgebra.

引用

页码：72 / 76

页数：5