The Local Multiplier Algebra: Blending Noncommutative Ring Theory and Functional Analysis
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.
KeywordsNoncommutative rings of quotients C*-algebras AW*-algebras local multiplier algebra injective envelope operator modules derivations
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