Distance between unitary orbits of normal elements in simple C*-algebras of real rank zero

2014/03/04 by Shanwen Hu, Hu, Shanwen, Huaxin Lin +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1403.0927

openalex publication_date 2014/03/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let x, y be two normal elements in a unital simple C*-algebra A. We introduce a function D_c(x, y) and show that in a unital simple AF-algebra there is a constant 1>C>0 such that C⋅ D_c(x, y)≤ \rm dist(\cal U(x),\cal U(y))≤ D_c(x,y), where \cal U(x) and \cal U(y) are the closures of the unitary orbits of x and of y, respectively. We also generalize this to unital simple C*-algebras with real rank zero, stable rank one and weakly unperforated K₀-group. More complicated estimates are given in the presence of non-trivial K₁-information.

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