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The Local Multiplier Algebra: Blending Noncommutative Ring Theory and Functional Analysis

  • Martin Mathieu
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

We discuss some basic features of the local multiplier algebra of a C*-algebra, the analytic analogue of the well-known Kharchenko-Martindale symmetric ring of quotients, and also the more recent maximal C*-algebra of quotients, which is the analytic companion to the Utumi-Lanning maximal symmetric ring of quotients, together with some of the applications to operator theory on C*-algebras. The emphasis lies in illustrating the interrelations between noncommutative ring theory and functional analysis.

Keywords

Noncommutative rings of quotients C*-algebras AW*-algebras local multiplier algebra injective envelope operator modules derivations 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Martin Mathieu
    • 1
  1. 1.Department of Pure MathematicsQueen’s University BelfastBelfastNorthern Ireland

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