Richard V. Kadison (1925–2018)
نویسندگان
چکیده
منابع مشابه
The Kadison-Singer Conjecture
We are given a large integer N , and a fixed basis {ei : 1 ≤ i ≤ N} for the space H = C . We are also given an N -by-N matrix H that has all its diagonal entries zero, and has norm one. If σ ⊆ {1, 2, . . . , N}, let Pσ be the projection onto the space Hσ := ∨{ei : i ∈ σ}. Call such a projection basic, and the range of a basic projection a basic subspace. For each constant 0 < γ < 1, we want to ...
متن کاملThe Other Kadison–singer Problem
Let H be `2 (over C) and let B(H) denote the C*-algebra of all bounded operators on H. Fix an orthonormal basis (en) for H. The atomic masa corresponding to this basis is `∞; equivalently, the algebra of all operators that are diagonalized by the basis (en). The projections in `∞ are exactly the projections onto subspaces spanned by a subset of {en}. That is, P(`∞) ∼= P(N) (here P(A) denotes th...
متن کاملKadison-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 کاملA Kadison–sakai Type Theorem
The celebrated Kadison–Sakai theorem states that every derivation on a von Neumann algebra is inner. In this paper, we prove this theorem for ultraweakly continuous ∗-σ-derivations, where σ is an ultraweakly continuous surjective ∗-linear mapping. We decompose a σ-derivation into a sum of an inner σ-derivation and a multiple of a homomorphism. The so-called ∗-(σ, τ)-derivations are also discussed.
متن کاملA Kadison–Dubois representation for associative rings
In this paper we give a general theorem that describes necessary and sufficient conditions for a module to satisfy the so–called Kadison–Dubois property. This is used to generalize Jacobi’s version of the Kadison–Dubois representation to associative rings. We apply this representation to obtain a noncommutative algebraic and geometric version of Putinar’s Positivstellensatz. We finish the paper...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 2019
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.1911782116