Distance Between Unitary Orbits of Self-Adjoint Elements in C*-Algebras of Tracial Rank One

Abstract

The note studies certain distance between unitary orbits. A result about Riesz interpolation property is proved in the first place. Weyl (1912) shows that dist(U(x), U(y)) =δ(x,y) for self-adjoint elements in matrixes. The author generalizes the result to C*-algebras of tracial rank one. It is proved that dist(U(x),U(y)) = D _c(x,y) in unital AT-algebras and in unital simple C*-algebras of tracial rank one, where x, y are self-adjoint elements and D _C (x, y) is a notion generalized from δ(x,y).

Keywords

Unitary orbits / Riesz interpolation property / Tracial rank one / D _c(x,y)

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