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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 $A$.

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

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