Duality and Normal Parts of Operator Modules
| dc.creator | Magajna, B. | |
| dc.date | 2003-07-07 | |
| dc.date | 2004-12-07 | |
| dc.date.accessioned | 2026-07-07T04:59:27Z | |
| dc.date.available | 2026-07-07T04:59:27Z | |
| dc.description | For an operator bimodule $X$ over von Neumann algebras $A\subseteq\bh$ and $B\subseteq\bk$, the space of all completely bounded $A,B$-bimodule maps from $X$ into $\bkh$, is the bimodule dual of $X$. Basic duality theory is developed with a particular attention to the Haagerup tensor product over von Neumann algebras. To $X$ a normal operator bimodule $\nor{X}$ is associated so that completely bounded $A,B$-bimodule maps from $X$ into normal operator bimodules factorize uniquely through $\nor{X}$. A construction of $\nor{X}$ in terms of biduals of $X$, $A$ and $B$ is presented. Various operator bimodule structures are considered on a Banach bimodule admitting a normal such structure. | |
| dc.description | The first version of the paper has been split into two parts, corrected and a few results added. This is the first part | |
| dc.identifier | https://arxiv.org/abs/math/0307079 | |
| dc.identifier | http://arxiv.org/abs/math/0307079 | |
| dc.identifier | J.F.A. 219/2, pp. 306--339, February 2005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67992 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L07, 46H25 (Primary), 47L25 (Secondary) | |
| dc.title | Duality and Normal Parts of Operator Modules | |
| dc.type | text |