Uniformity in -algebras
Tom 252 / 2020
Streszczenie
We introduce a notion of uniform structure on the set of all representations of a given separable, not necessarily commutative C^*-algebra \mathfrak A by introducing a suitable family of metrics on the set of representations of \mathfrak A and investigate its properties. We define the noncommutative analogue of the notion of the modulus of continuity of an element in a C^*-algebra and we establish its basic properties. We also deal with morphisms of C^*-algebras by defining two notions of uniform continuity and show their equivalence.