On a canonical lattice structure on the effect algebra of a von Neumann algebra
| dc.creator | de Groote, Hans F. | |
| dc.date | 2004-10-06 | |
| dc.date | 2005-12-27 | |
| dc.date.accessioned | 2026-07-07T06:38:32Z | |
| dc.date.available | 2026-07-07T06:38:32Z | |
| dc.description | Let R be a von Neumann algebra acting on a Hilbert space H and let R_sa be the set of selfadjoint elements of R. It is well known that R_sa is a lattice with respect to the usual partial order ≤ if and only if R is abelian. We define and study a new partial order on R_sa, the spectral order ≤_s, which extends ≤ on projections, is coarser than the usual one, but agrees with it on abelian subalgebras, and turns R_sa into a boundedly complete lattice. The effect algebra E(R) := {A | 0 ≤ A ≤ I} is then a complete lattice and we show that the mapping A --> R(A), where R(A) denotes the range projection of A, is a homomorphism from the lattice E(R) onto the projection lattice P(R) of A if and only if R is a finite von Neumann algebra. | |
| dc.description | 18 pages, no figures References added, slightly extended | |
| dc.identifier | https://arxiv.org/abs/math-ph/0410018 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0410018 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100770 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Operator Algebras | |
| dc.subject | Quantum Physics | |
| dc.subject | 46L10; 81Q10 | |
| dc.title | On a canonical lattice structure on the effect algebra of a von Neumann algebra | |
| dc.type | text |