Nest Algebras are Hyperfinite
نویسندگان
چکیده
منابع مشابه
Kadison-Singer algebras: hyperfinite case.
A new class of operator algebras, Kadison-Singer algebras (KS-algebras), is introduced. These highly noncommutative, non-self-adjoint algebras generalize triangular matrix algebras. They are determined by certain minimally generating lattices of projections in the von Neumann algebras corresponding to the commutant of the diagonals of the KS-algebras. A new invariant for the lattices is introdu...
متن کاملIrreducible Hyperfinite Ii1 Subfactors: Powers’ Algebras
We construct a series of inclusions of hyperfinite subfactors Pi in the centralizer R of Powers’ IIIt factor, Pi+1 ⊂ Pi ⊂ R. It is proven that: ∀i ∈ N, P ′ i ∩R = C, [Pi : Pi+1] ≥ λ = (1 + t) t Via an outer action of Z2 on R, we also construct an inclusion of hyperfinite II1 factors, M3 ⊂ M1 with the index equal to λ, such that the relative commutant M1 ∩M ′ 3 is four dimensional.
متن کاملTriangular Algebras and Ideals of Nest Algebras
Let %? be a separable Hubert space and !T c 3§(J%f) be an algebra of bounded operators. Say F is triangular if ^ n ^ * is a maximal abelian self-adjoint subalgebra (m.a.s.a.) of 3B{%?) and call this m.a.s.a. the diagonal of J7". A triangular algebra is maximal triangular if it is not properly contained in any triangular algebra. Triangular algebras of operators have been studied for 30 years no...
متن کاملThe Free Entropy Dimension of Hyperfinite Von Neumann Algebras
ABSTRACT. Suppose M is a hyperfinite von Neumann algebra with a tracial state φ and {a1, . . . , an} is a set of self-adjoint generators for M. We calculate δ0(a1, . . . , an), the modified free entropy dimension of {a1, . . . , an}. Moreover we show that δ0(a1, . . . , an) depends only on M and φ. Consequently δ0(a1, . . . , an) is independent of the choice of generators for M . In the course ...
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: Illinois Journal of Mathematics
سال: 1998
ISSN: 0019-2082
DOI: 10.1215/ijm/1255985616