1997/09/26 by Francesco Fidaleo, Fidaleo, Francesco
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #funct-an #hep-th #math.OA
paper · pdf · doi:10.48550/arxiv.funct-an/9709006
25 pages, LaTex, Some changes in the macroes
openalex publication_date 1997/09/26 · arxiv created 1997/10/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A characterization of the split property for an inclusion N⊂ M of W^*-factors with separable predual is established in terms of the canonical non-commutative L2 embedding considered in \citeB1,B2 \F2:a∈ N→ \DM,\Om1/4a\Om∈ L2(M,\Om) associated with an arbitrary fixed standard vector \Om for M. This characterization follows an analogous characterization related to the canonical non-commutative L1 embedding \F1:a∈ N→ (⋅\Om,JM,\Oma\Om)∈ L1(M,\Om) also considered in \citeB1,B2 and studied in \citeF. The split property for a Quantum Field Theory is characterized by equivalent conditions relative to the non-commutative embeddings \Fi, 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.