When is Every Quasi-Multiplier a Multiplier?
Operator Algebras
2018-12-31 v1 Functional Analysis
Abstract
We answer the title question for sigma-unital C*-algebras. The answer is that the algebra must be the direct sum of a dual C*-algebra and a C*-algebra satisfying a certain local unitality condition. We also discuss similar problems in the context of Hilbert C*-bimodules and imprimitivity bimodules and in the context of centralizers of Pedersen's ideal.
Cite
@article{arxiv.1812.11086,
title = {When is Every Quasi-Multiplier a Multiplier?},
author = {Lawrence G. Brown},
journal= {arXiv preprint arXiv:1812.11086},
year = {2018}
}