GEOMETRIC PRE-ORDERING ON C*-ALGEBRAS
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AbstractIt has been a successful practice to define a canonical pre-ordering on a normed space using the inclusion of faces of its closed dual unit ball. This pre-ordering reflects some geometric property in a natural way. In this article, we will give an algebraic description of this pre-ordering in the case of complex C*-algebras as well as that of their self-adjoint parts. In developing our theory we introduce the essential support of an element, which is closely related to the notion of peak projections studied recently by Blecher and Hay. As applications, we give some interesting facts about weak*-closed faces, and will identify the quasi-maximal elements and the quasi-minimal elements with respects to this pre-ordering. They are closely related to the extreme points and the smooth points of the unit sphere of the C*-algebra.
All Author(s) ListLeung CW, Ng CK, Wong NC
Journal nameJOURNAL OF OPERATOR THEORY
Year2010
Month12
Day1
Volume Number63
Issue Number1
PublisherTHETA FOUNDATION
Pages115 - 128
ISSN0379-4024
LanguagesEnglish-United Kingdom
KeywordsC*-algebra; essential support; exposure; Geometric pre-ordering; hermitian exposure; partial isometry; weak*-closed face
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2020-28-10 at 00:08