C*-algebras of infinite real rank

الأصل · EN

We introduce the notion of weakly (strongly) infinite real rank for unital C-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-algebra C(F∞) of the free group on countable number of generators has strongly infinite real rank.