Injective envelopes of continuous trace C*-algebras
by
Doug Farenick
University of Regina
Coauthors: Martin Argerami and Pedro Massey

If A is a postliminal (type I) C^*-algebra, then its injective envelope I(A) is a type I AW^*-algebra. The ideal J of I(A) generated by the abelian projections of I(A) is a liminal C^*-algebra with Hausdorff spectrum, and its multiplier algebra M(J) is I(A). Because J can be represented as a continuous C^*-bundle, the multiplier algebra of M(J)=I(A) is a C^*-algebra of bounded, strictly continuous operator fields on the spectrum of J. How is the spectrum of J determined from A? In particular, what is the relationship between the spectra of A and J if A is assumed to be a continuous C^*-bundle over a locally compact Hausdorff space? This talk will address such questions, with the overall aim of finding an explicit description of the injective envelopes and the local multiplier algebras of continuous trace C^*-algebras A.

Date received: April 4, 2008