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One-sided ideals and approximate identities in operator algebras | | David P. Blecher
; | | Date: |
16 Nov 2001 | | Subject: | Operator Algebras; Functional Analysis MSC-class: 47L30 47L45 47L25 | math.OA math.FA | | Abstract: | 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’. | | Source: | arXiv, math.OA/0111189 | | Services: | Forum | Review | PDF | Favorites | |
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