One-sided ideals and approximate identities in operator algebras
| dc.creator | Blecher, David P. | |
| dc.date | 2001-11-16 | |
| dc.date.accessioned | 2026-07-07T04:44:38Z | |
| dc.date.available | 2026-07-07T04:44:38Z | |
| dc.description | A left ideal of any $C^*$-algebra is an example of an operator algebra with a right contractive approximate identity (r.c.a.i.). Indeed left ideals in $C^*$-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 $C^*$-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'. | |
| dc.identifier | https://arxiv.org/abs/math/0111189 | |
| dc.identifier | http://arxiv.org/abs/math/0111189 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62669 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 47L30 47L45 47L25 | |
| dc.title | One-sided ideals and approximate identities in operator algebras | |
| dc.type | text |