Operator space structures and the split property II
| dc.creator | Fidaleo, Francesco | |
| dc.date | 1997-09-26 | |
| dc.date | 1997-10-07 | |
| dc.date.accessioned | 2026-07-07T09:02:57Z | |
| dc.date.available | 2026-07-07T09:02:57Z | |
| dc.description | A characterization of the split property for an inclusion $N\subset M$ of $W^*$-factors with separable predual is established in terms of the canonical non-commutative $L^2$ embedding considered in \cite{B1,B2} $$ \F_2:a\in N\to \D_{M,\Om}^{1/4}a\Om\in L^2(M,\Om) $$ associated with an arbitrary fixed standard vector $\Om$ for $M$. This characterization follows an analogous characterization related to the canonical non-commutative $L^1$ embedding $$ \F_1:a\in N\to (\cdot\Om,J_{M,\Om}a\Om)\in L^1(M,\Om) $$ also considered in \cite{B1,B2} and studied in \cite{F}. The split property for a Quantum Field Theory is characterized by equivalent conditions relative to the non-commutative embeddings $\F_i$, $i=1,2$, constructed by the modular Hamiltonian of a privileged faithful state such as e.g. the vacuum state. The above characterization would be also useful for theories on a curved space-time where there exists no a-priori privileged state. | |
| dc.description | 25 pages, LaTex, Some changes in the macroes | |
| dc.identifier | https://arxiv.org/abs/funct-an/9709006 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9709006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/148825 | |
| dc.subject | Functional Analysis | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Operator Algebras | |
| dc.title | Operator space structures and the split property II | |
| dc.type | text |