Operator spaces and residually finite-dimensional $C^\ast$-algebras

Details Operator spaces and residually finite-dimensional $C^\ast$-algebras Operator spaces and residually finite-dimensional $C^\ast$-algebras

1993-02-25

arxiv.org/abs/funct-an/9302007v1

Mathematics

Operator Algebras

7 pages, AmS TeX 2.1

Scientific paper

For every operator space $X$ the $C^\ast$-algebra containing it in a universal way is residually finite-dimensional (that is, has a separating family of finite-dimensional representations). In particular, the free $C^\ast$-algebra on any normed space so is. This is an extension of an earlier result by Goodearl and Menal, and our short proof is based on a criterion due to Exel and Loring.

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