Injective envelopes and local multiplier algebras of some spatial continuous trace C*-algebras

A precise description of the injective envelope of a spatial continuous trace C*-algebra A over a Stonean space Δ is given. The description is based on the notion of a weakly continuous Hilbert bundle, which we show herein to be a Kaplansky-Hilbert module over the abelian AW*-algebra C(Δ). 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.Fil: Argerami, Martin. University of Regina; Estados UnidosFil: Farenick, Douglas. University of Regina; Estados UnidosFil: Massey, Pedro Gustavo. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin