On *-similarity in C*-algebras
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Date
2020
Authors
Marcoux, Laurent
Radjavi, Heydar
Yahaghi, B.R.
Journal Title
Journal ISSN
Volume Title
Publisher
Instytut Matematyczny
Abstract
Two subsets X and Y of a unital C -algebra A are said to be -similar via
s 2 A1 if Y = s1Xs and Y = s1X s. We show that this relation imposes a certain
structure on the sets X and Y, and that under certain natural conditions (for example, if
X is bounded), -similar sets must be unitarily equivalent. As a consequence of our main
results, we present a generalized version of a well-known theorem of W. Specht.
Description
Published by the Institute of Mathematics Polish Academy of Sciences, Marcoux, L. W., Radjavi, H., & Yahaghi, B. R. (2020). On *-similarity in C*-algebras. Studia Mathematica, 252(1), 93–103. https://doi.org/10.4064/sm190102-29-4
Keywords
quasidiagonal *-similarity, Fuglede-Putnam theorem, Specht's theorem, unitary equivalence