One-sided ideals and approximate identities in operator algebras
Abstract
A left ideal of any -algebra is an example of an operator algebra with a right contractive approximate identity (r.c.a.i.). Indeed left ideals in -algebras may be characterized as the class of such operator algebras, which happen also to be triple systems. Conversely, we show here and in a sequel to this paper, that operator algebras with r.c.a.i. should be studied in terms of a certain left ideal of a -algebra. We study left ideals from the perspective of `Hamana theory' and using the multiplier algebras introduced by the author. More generally, we develop some general theory for operator algebras which have a 1-sided identity or approximate identity, including a Banach-Stone theorem for these algebras, and an analysis of the `multiplier operator algebra'.
Keywords
Cite
@article{arxiv.math/0111189,
title = {One-sided ideals and approximate identities in operator algebras},
author = {David P. Blecher},
journal= {arXiv preprint arXiv:math/0111189},
year = {2007}
}