# Journal of Operator Theory

Volume 86, Issue 2, Fall 2021 pp. 299-316.

Distance between unitary orbits in $C^*$-algebras with stable rank one and real rank zero**Authors**: George A. Elliott (1), Zhichao Liu (2)

**Author institution:**(1) Department of Mathematics, Univ. of Toronto, Toronto, M5S 2E4, Canada

(2) School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

**Summary:**Let $A$ be a $C^*$-algebra with stable rank one and real rank zero. In this paper, it is shown that the usual distance $d_U$ defined on the approximate unitary equivalence classes (or unitary orbits) of the positive elements in $A$ is equal to the distance $d_W$ defined on morphisms from Cuntz semigroup of $C_0(0,1]$ to the Cuntz semigrout of $A$.

**DOI:**http://dx.doi.org/10.7900/jot.2020apr21.2306

**Keywords:**unitary orbits, stable rank one, real rank zero, Birkhoff-Riesz interpolation

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