Destabilization

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3 Scopus citations

Abstract

This partly expository paper first supplies the details of a method of factoring a stable C*-algebra A as B⊗K in a canonical way. Then it is shown that this method can be put into a categorical framework, much like the crossed-product dualities, and that stabilization gives rise to an equivalence between the nondegenerate category of C*-algebras and a category of "K-algebras". We consider this equivalence as "inverting" the stabilization process, that is, a "destabilization".Furthermore, the method of factoring stable C*-algebras generalizes to Hilbert bimodules, and an analogous category equivalence between the associated enchilada categories is produced, giving a destabilization for C*-correspondences.Finally, we make a connection with (double) crossed-product duality.

Original languageEnglish (US)
Pages (from-to)62-81
Number of pages20
JournalExpositiones Mathematicae
Volume34
Issue number1
DOIs
StatePublished - 2016

Keywords

  • C*-correspondence
  • Category equivalence
  • Compact operators
  • Primary
  • Secondary
  • Stabilization

ASJC Scopus subject areas

  • Mathematics(all)

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