期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2007
卷号：2007
DOI：10.1155/2007/37186
出版社：Hindawi Publishing Corporation
摘要：In 1976, Kaplansky introduced the class JB*-algebras which includes all C*-algebras as a proper subclass. The notion of topological stable rank 1 for C*-algebras was originally introduced by M. A. Rieffel and was extensively
studied by various authors. In this paper, we extend this notion to general
JB*-algebras. We show that the complex spin factors are of tsr 1 providing an example of special JBW*-algebras for which the enveloping von Neumann algebras may not be of tsr 1. In the sequel, we prove that
every invertible element of a JB*-algebra 𝒥 is positive in certain isotope of 𝒥; if the algebra is finite-dimensional, then it is of tsr 1 and every element of 𝒥 is positive in some unitary isotope of 𝒥. Further, it is established that extreme points of the unit ball
sufficiently close to invertible elements in a JB*-algebra must be unitaries and that in any JB*-algebras of tsr 1, all extreme points of the unit ball are unitaries. In the end, we prove the coincidence between the
λ-function and λu-function on invertibles in a JB*-algebra.
