Injective Envelopes and Local Multiplier Algebras of Some Spatial Continuous Trace C*-Algebras
Operator Algebras
2012-07-09 v2
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.
Keywords
Cite
@article{arxiv.1003.5726,
title = {Injective Envelopes and Local Multiplier Algebras of Some Spatial Continuous Trace C*-Algebras},
author = {Martin Argerami and Douglas Farenick and Pedro Massey},
journal= {arXiv preprint arXiv:1003.5726},
year = {2012}
}
Comments
27 pages; many small corrections