Maximal C*-algebras of quotients and injective envelopes of C*-algebras

Pere Ara, Martin Mathieu

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7 Citations (Scopus)

Abstract

A new C*-enlargement of a C*-algebra A nested between the local multiplier algebra Mloc(A) of A and its injective envelope I(A) is introduced. Various aspects of this maximal C*-algebra of quotients, Qmax(A), are studied, notably in the setting of AW*-algebras. As a by-product we obtain a new example of a type I C*-algebra A such that Mloc(Mloc(A)) ≠ Mloc(A). © 2008 University of Houston.
Original languageEnglish
Pages (from-to)827-872
JournalHouston Journal of Mathematics
Volume34
Issue number3
Publication statusPublished - 18 Nov 2008

Keywords

  • AW*-algebra
  • Completely bounded module homomorphism
  • Hilbert C*-module
  • Injective envelope
  • Local multiplier algebra
  • Maximal C*-algebra of quotients

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