Marcoux, LaurentRadjavi, HeydarYahaghi, B.R.2024-01-312024-01-312020https://doi.org/10.4064/sm190102-29-4http://hdl.handle.net/10012/20322Published 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/sm190102-29-4Two subsets X and Y of a unital C -algebra A are said to be -similar via s 2 A􀀀1 if Y = s􀀀1Xs and Y = s􀀀1X 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.enAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/quasidiagonal *-similarityFuglede-Putnam theoremSpecht's theoremunitary equivalenceArticle