Centrally pure C*-algebras
Journal article, 2026
We show that a separable C⁎[jls-end-space/]-algebra A is Z[jls-end-space/]-stable if and only if its uncorrected central sequence algebra A′∩AU is pure, if and only if Kirchberg's central sequence algebra F(A) is pure.More generally, we show that a C⁎[jls-end-space/]-algebra A is separably Z[jls-end-space/]-stable if and only if the relative central sequence algebra B′∩AU is pure for every separable subalgebra B⊆AU[jls-end-space/].
Author
Francesc Perera
Centre de Recerca Matemàtica
Universitat Autonoma de Barcelona (UAB)
Hannes Thiel
University of Gothenburg
Chalmers, Mathematical Sciences, Analysis and Probability Theory
Eduard Vilalta Vila
Polytechnic University of Catalonia
Journal of Functional Analysis
0022-1236 (ISSN) 1096-0783 (eISSN)
Vol. 291 8 111578Subject Categories (SSIF 2025)
Mathematical Analysis
DOI
10.1016/j.jfa.2026.111578