Uniformity in $C^*$-algebras
Volume 252 / 2020
Studia Mathematica 252 (2020), 169-211
MSC: Primary 46L05.
DOI: 10.4064/sm180806-18-3
Published online: 16 December 2019
Abstract
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.
