Locally pre-𝐶*-equivalent algebras

Wu, Wei

doi:10.1090/S0002-9939-02-06686-8

Locally pre-$C$*-equivalent algebras
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Proc. Amer. Math. Soc. 131 (2003), 555-562 Request permission

Abstract:

We prove a weaker form of Cuntz’s theorem: every locally pre-$C^*$-equivalent Banach *-algebra is $C^*$-equivalent. Using this result, we obtain local conditions for the existence of an equivalent $C^*$-norm.

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