Extensions of pure states and projections of norm one

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Abstract

We show that the extension property for pure states of a C*-subalgebra B of a C*-algebra. A leads to the existence of a projection of norm one R: A --> B in the case where B is liminal with Hausdorff primitive ideal space. Furthermore, R is given by a "Dixmier process" in which the averaging is affected by a group of unitary elements in the centre of the multiplier algebra M(B). These results generalize earlier work of J. Anderson and the author for the case when B is a masa of a. Various applications are given in the contest of inductive limit algebras such as AF algebras and, more generally, Kumjian's ultraliminary C*-algebras. (C) 1999 Academic Press.

Original languageEnglish
Pages (from-to)24-43
Number of pages20
JournalJournal of Functional Analysis
Volume165
Publication statusPublished - 1999

Keywords

  • C*-algebras
  • pure state
  • unique extension
  • projection of norm one
  • AF algebra
  • ultraliminary
  • C-ASTERISK-ALGEBRAS
  • OPERATOR-ALGEBRAS
  • STAR-ALGEBRAS
  • FACTORIAL STATES
  • CSTAR-ALGEBRAS
  • REPRESENTATIONS
  • MULTIPLICITY
  • PRODUCTS
  • TRACE
  • MAPS

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