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

TL;DR

This paper characterizes the injective envelope and local multiplier algebra of certain continuous trace C*-algebras derived from Hilbert bundles over locally compact Hausdorff spaces, and proves the second-order local multiplier algebra is injective.

Contribution

It provides explicit descriptions of the injective envelope and local multiplier algebra for these C*-algebras, extending understanding of their structure.

Findings

Injective envelope determined for the class of C*-algebras studied

Local multiplier algebra explicitly characterized

Second-order local multiplier algebra shown to be injective

Abstract

We determine the injective envelope and local multiplier algebra of a continuous trace C*-algebra that arises from a continuous Hilbert bundle over an arbitrary locally compact Hausdorff space. In addition, we show that the second-order local multiplier algebra of any such algebra is injective.