On the (non)existence of states on orthogonally closed subspaces in an inner product space
| dc.creator | Chetcuti, E. | |
| dc.creator | Ptak, P. | |
| dc.date | 2003-01-16 | |
| dc.date.accessioned | 2026-07-07T04:54:29Z | |
| dc.date.available | 2026-07-07T04:54:29Z | |
| dc.description | Suppose that $S$ is an incomplete inner product space. A. Dvurečenskij shows that there are no finitely additive states on orthogonally closed subspaces, $F(S)$, of $S$ that are regular with respect to finitely dimensional spaces. In this note we show that the most important special case of the former result--the case of the evaluations given by vectors in the ``Gleason manner''--allows for a relatively simple proof. This result further reinforces the conjecture that there are no finitely additive states on $F(S)$ at all. | |
| dc.identifier | https://arxiv.org/abs/math/0301174 | |
| dc.identifier | http://arxiv.org/abs/math/0301174 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66271 | |
| dc.subject | Rings and Algebras | |
| dc.title | On the (non)existence of states on orthogonally closed subspaces in an inner product space | |
| dc.type | text |