Category: Operator algebras

Pisier–Ringrose inequality
In mathematics, Pisier–Ringrose inequality is an inequality in the theory of C*-algebras which was proved by Gilles Pisier in 1978 affirming a conjecture of John Ringrose. It is an extension of the Gr
Weak trace-class operator
In mathematics, a weak trace class operator is a compact operator on a separable Hilbert space H with singular values the same order as the harmonic sequence.When the dimension of H is infinite, the i
Nest algebra
In functional analysis, a branch of mathematics, nest algebras are a class of operator algebras that generalise the upper-triangular matrix algebras to a Hilbert space context. They were introduced by
Kadison transitivity theorem
In mathematics, Kadison transitivity theorem is a result in the theory of C*-algebras that, in effect, asserts the equivalence of the notions of topological irreducibility and algebraic irreducibility
Reflexive operator algebra
In functional analysis, a reflexive operator algebra A is an operator algebra that has enough invariant subspaces to characterize it. Formally, A is reflexive if it is equal to the algebra of bounded
Borchers algebra
In mathematics, a Borchers algebra or Borchers–Uhlmann algebra or BU-algebra is the tensor algebra of a vector space, often a space of smooth test functions. They were studied by H. J. Borchers, who s
Noncommutative measure and integration
Noncommutative measure and integration refers to the theory of weights, states, and traces on von Neumann algebras (Takesaki 1979 v. 2 p. 141).
Stinespring dilation theorem
In mathematics, Stinespring's dilation theorem, also called Stinespring's factorization theorem, named after W. Forrest Stinespring, is a result from operator theory that represents any completely pos
Octacube (sculpture)
The Octacube is a large, stainless steel sculpture displayed in the mathematics department of Pennsylvania State University in State College, PA. The sculpture represents a mathematical object called
Bratteli–Vershik diagram
In mathematics, a Bratteli–Veršik diagram is an ordered, essentially simple Bratteli diagram (V, E) with a homeomorphism on the set of all infinite paths called the Veršhik transformation. It is named
In mathematics, an O*-algebra is an algebra of possibly unbounded operators defined on a dense subspace of a Hilbert space. The original examples were described by and , who studied some examples of O
Operator algebra
In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of map
Bratteli diagram
In mathematics, a Bratteli diagram is a combinatorial structure: a graph composed of vertices labelled by positive integers ("level") and unoriented edges between vertices having levels differing by o
Kadison–Singer problem
In mathematics, the Kadison–Singer problem, posed in 1959, was a problem in functional analysis about whether certain extensions of certain linear functionals on certain C*-algebras were unique. The u
Jordan operator algebra
In mathematics, Jordan operator algebras are real or complex Jordan algebras with the compatible structure of a Banach space. When the coefficients are real numbers, the algebras are called Jordan Ban
Operator K-theory
In mathematics, operator K-theory is a noncommutative analogue of topological K-theory for Banach algebras with most applications used for C*-algebras.
Universal representation (C*-algebra)
In the theory of C*-algebras, the universal representation of a C*-algebra is a faithful representation which is the direct sum of the GNS representations corresponding to the states of the C*-algebra
Karoubi conjecture
In mathematics, the Karoubi conjecture is a conjecture by Max Karoubi that the algebraic and topological K-theories coincide on C* algebras spatially tensored with the algebra of compact operators. It
Operator system
Given a unital C*-algebra , a *-closed subspace S containing 1 is called an operator system. One can associate to each subspace of a unital C*-algebra an operator system via . The appropriate morphism
Calkin correspondence
In mathematics, the Calkin correspondence, named after mathematician John Williams Calkin, is a bijective correspondence between two-sided ideals of bounded linear operators of a separable infinite-di
Dirac–von Neumann axioms
In mathematical physics, the Dirac–von Neumann axioms give a mathematical formulation of quantum mechanics in terms of operators on a Hilbert space. They were introduced by Paul Dirac in 1930 and John
Planar algebra
In mathematics, planar algebras first appeared in the work of Vaughan Jones on the standard invariant of a II1 subfactor. They also provide an appropriate algebraic framework for many knot invariants