A new uniform structure for Hilbert C∗-modules.

We introduce and study some new uniform structures for Hilbert C ∗ -modules over a C ∗ -algebra A. In particular, we prove that in some cases they have the same totally bounded sets. To define one of them, we introduce a new class of A -functionals: locally adjointable functionals, which have interesting properties in this context and seem to be of independent interest. A relation between these uniform structures and the theory of A -compact operators is established. [ABSTRACT FROM AUTHOR]