Extensions of pure C*-algebras
Francesc Perera, Hannes Thiel, Eduard Vilalta

TL;DR
This paper investigates the conditions under which pure C*-algebras maintain their purity when extended or decomposed, and applies these results to stable multiplier algebras of free group C*-algebras.
Contribution
It establishes a characterization of pure C*-algebras via their ideals and quotients, and explores the preservation of comparison and divisibility properties in extensions.
Findings
A C*-algebra is pure if and only if its ideal and quotient are pure.
Permanence of comparison and divisibility properties in extensions is studied.
Stable multiplier algebras of reduced free group C*-algebras are shown to be pure.
Abstract
Given a closed ideal in a C*-algebra , we show that is pure if and only if and are pure. More generally, we study permanence of comparison and divisibility properties when passing to extensions. As an application we show that stable multiplier algebras of reduced free group C*-algebras are pure.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Banach Space Theory · Holomorphic and Operator Theory
