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arXiv · 1805.05998

Uniformity in $C^*$-algebras

Adam Wegert
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Abstract

We introduce a notion of a uniform structure on the set of all representations of a given separable, not necessarilly 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 $C^*$-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.

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Adam Wegert. 2018-05-15. Uniformity in $C^*$-algebras. https://arxiv.org/abs/1805.05998

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