Normal conditional expectations of finite index and sets of modular generators
| dc.creator | Frank, Michael | |
| dc.date | 1998-09-26 | |
| dc.date | 2000-02-09 | |
| dc.date.accessioned | 2026-07-07T05:26:10Z | |
| dc.date.available | 2026-07-07T05:26:10Z | |
| dc.description | Normal conditional expectations E: M --> N in M of finite index on von Neumann algebras M with discrete center are investigated to find an estimate for the minimal number of generators of M as a Hilbert N-module. Analyzing the case of M being finite type I with discrete center we obtain that these von Neumann algebras M are always finitely generated Hilbert N-modules with a minimal generator set consisting of at most [K(E)]^2 generators, where [.] denotes the integer part of a real number and K(E) = {K: K.E-id_M >= 0}. This result contrasts remarkable examples by P. Jolissaint and S. Popa showing the existence of normal conditional expectations of finite index on certain type II_1 von Neumann algebras with center l_\infty which are not algebraically of finite index in the sense of Y. Watatani. We show that estimates of the minimal number of module generators by a function of [K(E)] cannot exist for certain type II_1 von Neumann algebras with non-trivial center. | |
| dc.description | 7 pages, minor changes and additions, complemented list of literature | |
| dc.identifier | https://arxiv.org/abs/math/9809152 | |
| dc.identifier | http://arxiv.org/abs/math/9809152 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77449 | |
| dc.subject | Operator Algebras | |
| dc.title | Normal conditional expectations of finite index and sets of modular generators | |
| dc.type | text |