C*-algebras of infinite real rank

Details C*-algebras of infinite real rank C*-algebras of infinite real rank

2002-05-14

arxiv.org/abs/math/0205142v1

Mathematics

General Topology

9 pages

Scientific paper

We introduce the notion of weakly (strongly) infinite real rank for unital $C^{\ast}$-algebras. It is shown that a compact space $X$ is weakly (strongly) infine-dimensional if and only if $C(X)$ has weakly (strongly) infinite real rank. Some other properties of this concept are also investigated. In particular, we show that the group $C^{\ast}$-algebra $C^{\ast}({\mathbb F}_{\infty})$ of the free group on countable number of generators has strongly infinite real rank.

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