Injective Envelopes and Local Multiplier Algebras of Some Spatial Continuous Trace C*-Algebras

Abstract

A precise description of the injective envelope of a spatial continuous trace C*-algebra A over a Stonean space Delta is given. The description is based on the notion of a weakly continuous Hilbert bundle, which we show to be a Kaplansky--Hilbert module over the abelian AW*-algebra C(Delta). We then use the description of the injective envelope of A to study the first- and second-order local multiplier algebras of A. In particular, we show that the second-order local multiplier algebra of A is precisely the injective envelope of A.

27 pages; many small corrections

References in corpus (5)

• Injective Envelopes of $C^{\ast }$-algebras as Operator Modules
• Injective envelopes and local multiplier algebras of C*-algebras
• Maximal C*-algebras of quotients and injective envelopes of C*-algebras
• When is the second local multiplier algebra of a C*-algebra equal to the first?
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Cited by in corpus (2)

• When is the second local multiplier algebra of a C*-algebra equal to the first?
• The second local multiplier algebra of a separable C*-algebra