Multipliers of operator spaces, and the injective envelope
| dc.creator | Blecher, David P. | |
| dc.creator | Paulsen, Vern I. | |
| dc.date | 1999-09-07 | |
| dc.date | 2000-01-26 | |
| dc.date.accessioned | 2026-07-07T05:30:42Z | |
| dc.date.available | 2026-07-07T05:30:42Z | |
| dc.description | We study the injective envelope I(X) of an operator space X, showing amongst other things that it is a self-dual C$^*-$module. We describe the diagonal corners of the injective envelope of the canonical operator system associated with X. We prove that if X is an operator $A-B$-bimodule, then A and B can be represented completely contractively as subalgebras of these corners. Thus, the operator algebras that can act on X are determined by these corners of I(X) and consequently bimodules actions on X extend naturally to actions on I(X). These results give another characterization of the multiplier algebra of an operator space, which was introduced by the first author, and a short proof of a recent characterization of operator modules, and a related result. As another application, we extend Wittstock's module map extension theorem, by showing that an operator $A-B$-bimodule is injective as an operator $A-B$-bimodule if and only if it is injective as an operator space. | |
| dc.description | Revised version, January 21 2000 | |
| dc.identifier | https://arxiv.org/abs/math/9909041 | |
| dc.identifier | http://arxiv.org/abs/math/9909041 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79074 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46M10; 47D15 | |
| dc.title | Multipliers of operator spaces, and the injective envelope | |
| dc.type | text |