In mathematics, specifically in order theory and functional analysis, the order dual of an ordered vector space X {\displaystyle X} is the set Pos ⁡ (...

inverse, opposite, or converse. Duality (order theory), duality principle for ordered sets Order dual (functional analysis), set of all differences of any...

Hilbert spaces. Consequently, the dual space is an important concept in functional analysis. Early terms for dual include polarer Raum [Hahn 1927], espace...

\mathbb {K} } . In mathematics, duality is the study of dual systems and is important in functional analysis. Duality plays crucial roles in quantum mechanics...

(Boolean algebra) Duality principle for sets Duality principle (optimization theory) Lagrange duality Duality principle in functional analysis, used in large...

In mathematics, specifically in order theory and functional analysis, the order topology of an ordered vector space ( X , ≤ ) {\displaystyle (X,\leq )}...

there are sufficient continuous linear functionals defined on every normed vector space in order to study the dual space. Another version of the Hahn–Banach...

of scalars (that is, it is an element of the dual space V ∗ {\displaystyle V^{*}} ) In functional analysis and related fields, it refers to a mapping from...

operations (often denoted Hom(X,V)). One such space is the dual space of X: the set of linear functionals X → F with addition and scalar multiplication defined...

In mathematics, particularly in functional analysis, the closed graph theorem is a result connecting the continuity of a linear operator to a topological...

linear functionals from V to k is itself a vector space over k with addition and scalar multiplication defined pointwise. This space is called the dual space...

found a series of applications in Functional analysis and Geometry, including the generalization of Pontryagin duality for non-commutative topological groups...

in order theory and functional analysis, the order bound dual of an ordered vector space X {\displaystyle X} is the set of all linear functionals on X...

Milman, Vitali (2008), "The concept of duality for measure projections of convex bodies", Journal of Functional Analysis, 254 (10): 2648–66, CiteSeerX 10.1...

In mathematics, in the field of functional analysis, a Minkowski functional (after Hermann Minkowski) or gauge function is a function that recovers a...

Functional magnetic resonance imaging or functional MRI (fMRI) measures brain activity by detecting changes associated with blood flow. This technique...

Dualism in terms of politics, refers to specific political concepts that are related to the functional or structural duality of a particular political...

f^{-1}(y)} is a connected subspace of X . {\displaystyle X.} In functional analysis on a topological vector space X {\displaystyle X} , a (possibly non-linear)...

success of Hilbert space methods ushered in a very fruitful era for functional analysis. Apart from the classical Euclidean vector spaces, examples of Hilbert...

In mathematics, more specifically in functional analysis, a Banach space (/ˈbɑː.nʌx/, Polish pronunciation: [ˈba.nax]) is a complete normed vector space...

specifically in order theory and functional analysis, a subset A {\displaystyle A} of an ordered vector space is said to be order complete in X {\displaystyle...

least temporary conflict before reintegration (ibid). "The fact that functional analysis can be seen by some as inherently conservative and by others as inherently...

In functional analysis and related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation...

(functional analysis) Banach–Alaoglu theorem (functional analysis) Banach–Mazur theorem (functional analysis) Banach–Steinhaus theorem (functional analysis)...

topology—[that] echos throughout functional analysis.” In 1912, Helly proved that the unit ball of the continuous dual space of C ( [ a , b ] ) {\displaystyle...

In mathematics, particularly functional analysis, James' theorem, named for Robert C. James, states that a Banach space X {\displaystyle X} is reflexive...

numerical analysis topics. Validated numerics Iterative method Rate of convergence — the speed at which a convergent sequence approaches its limit Order of accuracy...

In mathematics, particularly in functional analysis, the Marcinkiewicz interpolation theorem, discovered by Józef Marcinkiewicz (1939), is a result bounding...

power set lattice of some set. Another variant, Stone's duality, states that there exists a duality (in the sense of an arrow-reversing equivalence) between...

disciplines of in functional analysis and order theory, a Banach lattice (X,‖·‖) is a complete normed vector space with a lattice order, ≤ {\displaystyle...