Distance between unitary orbits of normal elements in simple [formula omitted]-algebras of real rank zero

Abstract

Let x,y be two normal elements in a unital simple C⁎-algebra A. We introduce a function Dc(x,y) and show that in a unital simple AF-algebra there is a constant 1>C>0 such thatC⋅Dc(x,y)≤dist(U(x),U(y))≤Dc(x,y), where U(x) and 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.