On Galois Correspondence and Non-Commutative Martingales
| dc.creator | Saffary, Timor | |
| dc.date | 2008-12-22 | |
| dc.date | 2008-12-23 | |
| dc.date.accessioned | 2026-07-07T12:21:06Z | |
| dc.date.available | 2026-07-07T12:21:06Z | |
| dc.description | The subject of this thesis is Galois correspondence for von Neumann algebras and its interplay with non-commutative probability theory. After a brief introduction to representation theory for compact groups, in particular to Peter-Weyl theorem, and to operator algebras, including von Neumann algebras, automorphism groups, crossed products and decomposition theory, we formulate first steps of a non-commutative version of probability theory and introduce non-abelian analogues of stochastic processes and martingales. The central objects are a von Neumann algebra $\Ma$ and a compact group $\Gr$ acting on $\Ma$, for which we give in three consecutive steps, i.e. for inner, spatial and general automorphism groups one-to-one correspondences between subgroups of $\Gr$ and von Neumann subalgebras of $\Ma$. Furthermore, we identify non-abelian martingales in our approach and prove for them a convergence theorem. | |
| dc.identifier | https://arxiv.org/abs/0812.3943 | |
| dc.identifier | http://arxiv.org/abs/0812.3943 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213260 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.title | On Galois Correspondence and Non-Commutative Martingales | |
| dc.type | text |