Injective and projective Hilbert C*-modules, and C*-algebras of compact operators
| dc.creator | Frank, Michael | |
| dc.creator | Paulsen, Vern I. | |
| dc.date | 2006-11-12 | |
| dc.date | 2008-02-18 | |
| dc.date.accessioned | 2026-07-07T09:21:18Z | |
| dc.date.available | 2026-07-07T09:21:18Z | |
| dc.description | We consider projectivity and injectivity of Hilbert C*-modules in the categories of Hilbert C*-(bi-)modules over a fixed C*-algebra of coefficients (and another fixed C*-algebra represented as bounded module operators) and bounded (bi-)module morphisms, either necessarily adjointable or arbitrary ones. As a consequence of these investigations, we obtain a set of equivalent conditions characterizing C*-subalgebras of C*-algebras of compact operators on Hilbert spaces in terms of general properties of Hilbert C*-modules over them. Our results complement results recently obtained by B. Magajna, J. Schweizer and M. Kusuda. In particular, all Hilbert C*-(bi-)modules over C*-algebras of compact operators on Hilbert spaces are both injective and projective in the categories we consider. For more general C*-algebras we obtain classes of injective and projective Hilbert C*-(bi-)modules. | |
| dc.description | 28 pages, Proposition 3.4 corrected after receiving remarks from Hanfeng Li, thanks for pointing out the errors. Some minor corrections in formulations. 15 references added | |
| dc.identifier | https://arxiv.org/abs/math/0611349 | |
| dc.identifier | http://arxiv.org/abs/math/0611349 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154975 | |
| dc.subject | Operator Algebras | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 46L08; 46H25 | |
| dc.title | Injective and projective Hilbert C*-modules, and C*-algebras of compact operators | |
| dc.type | text |