A topological characterization of linearity for quasi-traces

Bunce, L.; Wright, J.

doi:10.1090/S0002-9939-96-03288-1

A topological characterization of linearity for quasi-traces
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by L. J. Bunce and J. D. Maitland Wright PDF

Proc. Amer. Math. Soc. 124 (1996), 2377-2381 Request permission

Abstract:

Let $\mathcal A$ be a $C^\ast$-algebra, and let $\mu$ be a (local) quasi-trace on $\mathcal A$. Then $\mu$ is linear if, and only if, the restriction of $\mu$ to the closed unit ball of $\mathcal A$ is uniformly weakly continuous.

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