Geodesic
Elements of $C^{\ast }$-algebras Attaining their Norm in a Finite-dimensional Representation
Canadian journal of mathematics, Tome 71 (2019) no. 1, pp. 93-111

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DOI

We characterize the class of RFD $C^{\ast }$-algebras as those containing a dense subset of elements that attain their norm under a finite-dimensional representation. We show further that this subset is the whole space precisely when every irreducible representation of the $C^{\ast }$-algebra is finite-dimensional, which is equivalent to the $C^{\ast }$-algebra having no simple infinite-dimensional AF subquotient. We apply techniques from this proof to show the existence of elements in more general classes of $C^{\ast }$-algebras whose norms in finite-dimensional representations fit certain prescribed properties.
DOI : 10.4153/CJM-2017-040-x
Mots-clés : AF-telescopes, RFD, projective 
Courtney, Kristin; Shulman, Tatiana. Elements of $C^{\ast }$-algebras Attaining their Norm in a Finite-dimensional Representation. Canadian journal of mathematics, Tome 71 (2019) no. 1, pp. 93-111. doi: 10.4153/CJM-2017-040-x
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     title = {Elements of $C^{\ast }$-algebras {Attaining} their {Norm} in a {Finite-dimensional} {Representation}},
     journal = {Canadian journal of mathematics},
     pages = {93--111},
     year = {2019},
     volume = {71},
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     doi = {10.4153/CJM-2017-040-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-040-x/}
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