Vol. 13, No. 7, 2020

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$C^{*}$-algebras isomorphically representable on $l^{p}$

March T. Boedihardjo

Vol. 13 (2020), No. 7, 2173–2181

Let p (1,){2}. We show that every homomorphism from a C-algebra 𝒜 into B(lp(J)) satisfies a compactness property where J is any set. As a consequence, we show that a C-algebra 𝒜 is isomorphic to a subalgebra of B(lp(J)), for some set J, if and only if 𝒜 is residually finite-dimensional.

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$l^p$ space, $C^*$-algebra
Mathematical Subject Classification 2010
Primary: 46H20
Received: 29 December 2018
Revised: 19 June 2019
Accepted: 6 September 2019
Published: 10 November 2020
March T. Boedihardjo
Department of Mathematics
University of California
Los Angeles, CA
United States