Limits of vector functionals

Robert J Archbold, M. H. Shah

Research output: Contribution to journalArticle

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Abstract

For vector functionals on a C*-algebra of operators, we prove an analogue of Glimm's vector state space theorem. We deduce that a C*-algebra is prime and antiliminal if and only if the pure functionals are w*-dense in the unit ball of the dual. We also give a necessary and sufficient condition for a convex combination of inequivalent pure functionals to be a w*-limit of pure functionals.

Original languageEnglish
Pages (from-to)39-51
Number of pages12
JournalJournal of Operator Theory
Volume45
Publication statusPublished - 2001

Keywords

  • C*-algebra
  • vector functional
  • pure functional
  • antiliminal
  • prime
  • PURE STATES

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