Resumen de A C*-analogue of Kazhdan's property (T)

A. A. Pavlov

• This paper deals with a ¿naive¿ way of generalizing Kazhdan's property (T) to C*-algebras. Our approach differs from the approach of Connes and Jones, which has already demonstrated its utility. Nevertheless, it turns out that our approach is applicable to a rather subtle question in the theory of C*-Hilbert modules. Namely, we prove that a separable unital C*-algebra A has property MI (module infinite¿i.e. any countably generated self-dual Hilbert module over A is finitely generated and projective) if and only if A does not satisfy our definition of property (T). The commutative case was studied in an earlier paper.