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dc.contributor.authorMarcoux, Laurent W.
dc.contributor.authorZhang, Yuanhang 16:40:53 (GMT) 16:40:53 (GMT)
dc.descriptionThe final publication is available at Elsevier via © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 licenseen
dc.description.abstractSpecht's Theorem states that two matrices A and B in Mn(C) are unitarily equivalent if and only if tr(w(A;A )) = tr(w(B;B )) for all words w(x; y) in two non-commuting variables x and y. In this article we examine to what extent this trace condition characterises approximate unitary equivalence in uniformly hyper nite (UHF) C -algebras. In particular, we show that given two elements a; b of the universal UHF algebra Q which generate C -algebras satisfying the UCT, they are approximately unitarily equivalent if and only if (w(a; a )) = (w(b; b )) for all words w(x; y) in two non-commuting variables (where denotes the unique tracial state on Q), while there exist two elements a; b in the UHF-algebra M21 which fail to be approximately unitarily equivalent despite the fact that they satisfy the trace condition. We also examine a consequence of these results for ampliations of matrices.en
dc.description.sponsorshipL.W. Marcoux's research is supported in part by NSERC (Canada); Y.H. Zhang's research is supported in part by National Natural Science Foundation of China (Nos.: 12071174, 11671167), Science and Technology Development Project of Jilin Province (No.: 20190103028JH).en
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.subjectspecht's theoremen
dc.subjectapproximate unitary equivalenceen
dc.subjectapproximate absolute value conditionen
dc.titleOn Specht's Theorem in UHF C⁎-algebrasen
dcterms.bibliographicCitationMarcoux, L. W., & Zhang, Y. (2021). On Specht’s Theorem in UHF C⁎-algebras. Journal of Functional Analysis, 280(1), 108778.
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Pure Mathematicsen

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