- Abstract algebra
- >
- Algebraic structures
- >
- Algebras
- >
- Operator algebras

- Fields of abstract algebra
- >
- Representation theory
- >
- Algebras
- >
- Operator algebras

- Group theory
- >
- Representation theory
- >
- Algebras
- >
- Operator algebras

- Mathematical analysis
- >
- Fields of mathematical analysis
- >
- Functional analysis
- >
- Operator algebras

- Mathematical analysis
- >
- Functions and mappings
- >
- Functional analysis
- >
- Operator algebras

- Mathematical objects
- >
- Functions and mappings
- >
- Functional analysis
- >
- Operator algebras

- Mathematical relations
- >
- Functions and mappings
- >
- Functional analysis
- >
- Operator algebras

- Mathematical structures
- >
- Algebraic structures
- >
- Algebras
- >
- 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

O*-algebra

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

© 2023 Useful Links.