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

MARTIN ARGERAMI; DOUGLAS FARENICK; PEDRO G. MASSEY

QUARTERLY JOURNAL OF MATHEMATICS

OXFORD UNIV PRESS

Lugar: Oxford; Año: 2010 p. 1 - 16

0033-5606

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