A Morita theorem for dual operator algebras
| dc.creator | Kashyap, Upasana | |
| dc.date | 2008-06-17 | |
| dc.date | 2008-10-17 | |
| dc.date.accessioned | 2026-07-07T10:10:31Z | |
| dc.date.available | 2026-07-07T10:10:31Z | |
| dc.description | We prove that two dual operator algebras are weak$^*$ Morita equivalent if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weak$^*$-continuous on appropriate morphism spaces. Moreover, in a fashion similar to the operator algebra case, we characterize such functors as the module normal Haagerup tensor product with an appropriate weak$^*$ Morita equivalence bimodule. We also develop the theory of the $W^*$-dilation, which connects the non-selfadjoint dual operator algebra with the $W^*$-algebraic framework. In the case of weak$^*$ Morita equivalence, this $W^*$-dilation is a $W^*$-module over a von Neumann algebra generated by the non-selfadjoint dual operator algebra. The theory of the $W^*$-dilation is a key part of the proof of our main theorem. | |
| dc.description | 21 pages | |
| dc.identifier | https://arxiv.org/abs/0806.2704 | |
| dc.identifier | http://arxiv.org/abs/0806.2704 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171622 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.title | A Morita theorem for dual operator algebras | |
| dc.type | text |