#### 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
##### Abstract

Let $p\in \left(1,\infty \right)\setminus \left\{2\right\}$. We show that every homomorphism from a ${C}^{\ast }$-algebra $\mathsc{𝒜}$ into $B\left({l}^{p}\left(J\right)\right)$ satisfies a compactness property where $J$ is any set. As a consequence, we show that a ${C}^{\ast }$-algebra $\mathsc{𝒜}$ is isomorphic to a subalgebra of $B\left({l}^{p}\left(J\right)\right)$, for some set $J$, if and only if $\mathsc{𝒜}$ is residually finite-dimensional.

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$l^p$ space, $C^*$-algebra