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- W2011740136 abstract "We give a sufficient condition for a $^*$-algebra with a specified basis to have an enveloping $C^*$-algebra. Particularizing to the setting of a Hecke algebra $h(G,gm)$, we show that under a suitable assumption not only we can assure that an enveloping $C^*$-algebra $C^*(G, gm)$ exists, but also that it coincides with $C^*(L^1(G,gm))$, the enveloping $C^*$-algebra of the $L^1$-Hecke algebra. Our methods are used to show the existence of $C^*(G, gm)$ and isomorphism with $C^*(L^1(G,gm))$ for several classes of Hecke algebras. Most of the classes which are known to satisfy these properties are covered by this approach, and we also describe some new ones." @default.
- W2011740136 created "2016-06-24" @default.
- W2011740136 creator A5075048884 @default.
- W2011740136 date "2012-01-03" @default.
- W2011740136 modified "2023-10-18" @default.
- W2011740136 title "On enveloping C*-algebras of Hecke algebras" @default.
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- W2011740136 doi "https://doi.org/10.48550/arxiv.1201.0709" @default.
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