Direct integrals and Hilbert W*-Modules
| dc.creator | Frank, Michael | |
| dc.date | 1993-12-06 | |
| dc.date.accessioned | 2026-07-07T09:13:26Z | |
| dc.date.available | 2026-07-07T09:13:26Z | |
| dc.description | Investigating the direct integral decomposition of von Neumann algebras of bounded module operators on self-dual Hilbert W*-moduli an equivalence principle is obtained which connects the theory of direct disintegration of von Neumann algebras on separable Hilbert spaces and the theory of von Neumann representations on self-dual Hilbert {\bf A}-moduli with countably generated {\bf A}-pre-dual Hilbert {\bf A}-module over commutative separable W*-algebras {\bf A}. Examples show posibilities and bounds to find more general relations between these two theories, (cf. R. Schaflitzel's results). As an application we prove a Weyl--Berg--Murphy type theorem: For each given commutative W*-algebra {\bf A} with a special approximation property (*) every normal bounded {\bf A}-linear operator on a self-dual Hilbert {\bf A}-module with countably generated {\bf A}-pre-dual Hilbert {\bf A}-module is decomposable into the sum of a diagonalizable normal and of a ''compact'' bounded {\bf A}-linear operator on that module. | |
| dc.description | 20 pages, LATEX file, preprint 23/91, NTZ, Univ. Leipzig, Germany | |
| dc.identifier | https://arxiv.org/abs/funct-an/9312002 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9312002 | |
| dc.identifier | Problems in algebra, geometry and discrete mathematics (in russian), Moscow State University, Fakulty of Mechanics and Mathematics, 1992, 162-177 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152326 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.title | Direct integrals and Hilbert W*-Modules | |
| dc.type | text |