Gleason’s theorem for type I von Neumann algebras
نویسندگان
چکیده
منابع مشابه
Kochen-Specker theorem for von Neumann algebras
The Kochen-Specker theorem has been discussed intensely ever since its original proof in 1967. It is one of the central no-go theorems of quantum theory, showing the non-existence of a certain kind of hidden states models. In this paper, we first offer a new, non-combinatorial proof for quantum systems with a type In factor as algebra of observables, including I∞. Afterwards, we give a proof of...
متن کاملA double commutant theorem for Murray-von Neumann algebras.
Murray-von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra A of the Murray-von Neumann algebra A(f)(R) associated with a finite von Neumann algebra R is the Murray-von Neumann algebra A(f)(A(0)), wh...
متن کاملStructure of derivations on various algebras of measurable operators for type I von Neumann algebras
Given a von Neumann algebra M denote by S(M) and LS(M) respectively the algebras of all measurable and locally measurable operators affiliated with M. For a faithful normal semi-finite trace τ on M let S(M, τ) (resp. S0(M, τ)) be the algebra of all τ -measurable (resp. τ -compact) operators from S(M). We give a complete description of all derivations on the above algebras of operators in the ca...
متن کاملvon Neumann Algebras
For every selfadjoint operator T in the Hilbert space H, f(T) makes sense not only in the obvious case where / is a polynomial but also if / is just measurable, and if fn(x)-+f(x) for all x£R (with (/,) bounded) then fn(T)-+f(T) weakly, i.e. <fn(T)£9i)+<f(T)£9ti)V£9fiCH. Moreover the set {f(T)9 f measurable} is the set of all operators S in H invariant under all unitary transformations of H whi...
متن کاملVon Neumann Algebras
The purpose of these notes is to provide a rapid introduction to von Neumann algebras which gets to the examples and active topics with a minimum of technical baggage. In this sense it is opposite in spirit from the treatises of Dixmier [], Takesaki[], Pedersen[], Kadison-Ringrose[], Stratila-Zsido[]. The philosophy is to lavish attention on a few key results and examples, and we prefer to make...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1982
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1982.100.473