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

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

2010-03-30

arxiv.org/abs/1003.5726v2

Mathematics

Operator Algebras

27 pages; many small corrections

Scientific paper

10.1093/qmath/haq037

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.

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