In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace...

that bear Banach's name include Banach spaces, Banach algebras, Banach measures, the Banach–Tarski paradox, the Hahn–Banach theorem, the Banach–Steinhaus...

The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in three-dimensional space, there exists...

then the Hahn–Banach theorem may sometimes be used to show that an extension exists. However, the extension may not be unique. Closed graph theorem (functional...

Hahn–Banach theorem the open mapping theorem the closed graph theorem the uniform boundedness principle, also known as the Banach–Steinhaus theorem....

existence of L-semi-inner products relies on the non-constructive Hahn–Banach theorem. L-semi-inner products are a generalization of inner products, which...

Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem...

Democrat magazine Der Kampf. Hahn's contributions to mathematics include the Hahn–Banach theorem and (independently of Banach and Steinhaus) the uniform...

Sublinear functions are often encountered in the context of the Hahn–Banach theorem. A real-valued function p : X → R {\displaystyle p:X\to \mathbb {R}...

name Banach functional is sometimes used, reflecting that they are most commonly used when applying a general formulation of the Hahn–Banach theorem. The...

and Hilbert space theory, vector-valued Hahn–Banach theorems are generalizations of the Hahn–Banach theorems from linear functionals (which are always...

analysis, the open mapping theorem, also known as the Banach–Schauder theorem or the Banach theorem (named after Stefan Banach and Juliusz Schauder), is...

In functional analysis, a field of mathematics, the Banach–Mazur theorem is a theorem roughly stating that most well-behaved normed spaces are subspaces...

the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space...

analysis and related branches of mathematics, the Banach–Alaoglu theorem (also known as Alaoglu's theorem) states that the closed unit ball of the dual space...

\limsup _{n\to \infty }x_{n}.} The existence of Banach limits is usually proved using the Hahn–Banach theorem (analyst's approach), or using ultrafilters...

gives a short proof of Bishop's theorem using the Krein–Milman theorem in an essential way, as well as the Hahn–Banach theorem: the process of Louis de Branges...

The Hahn–Banach family of theorems gives conditions under which this extension can be done. For example, Hahn–Banach dominated extension theorem(Rudin...

functional φ: E → R such that φ(x) > 0. The Hahn–Banach theorem can be deduced from the M. Riesz extension theorem. Let V be a linear space, and let N be a...

include polarer Raum [Hahn 1927], espace conjugué, adjoint space [Alaoglu 1940], and transponierter Raum [Schauder 1930] and [Banach 1932]. The term dual...

a convex local base for the zero vector is strong enough for the Hahn–Banach theorem to hold, yielding a sufficiently rich theory of continuous linear...

family Hahn series, a mathematical formal infinite series Hahn–Banach theorem, theory in functional analysis All pages with titles containing Hahn Han (disambiguation)...

{\displaystyle 0} function (Rudin 1991, §1.47). In particular, the Hahn-Banach theorem does not hold for L p ( [ 0 , 1 ] ) {\displaystyle L^{p}([0,1])}...

material on amenable groups, connections to the axiom of choice and the Hahn–Banach theorem. Three appendices describe Euclidean groups, Jordan measure, and...

countable set. The Hahn–Banach theorem. In ZF, the Hahn–Banach theorem is strictly weaker than the ultrafilter lemma. The Banach–Tarski paradox. In fact...

variant of Hahn–Banach theorem: Theorem Let S 1 {\displaystyle S_{1}} and S 2 {\displaystyle S_{2}} be disjoint convex closed sets in a real Banach space and...

for example aspects relating to convexity and the Hahn–Banach theorem are different. Ostrowski's theorem, due to Alexander Ostrowski (1916), states that...

acceptable in constructive analysis. A famous example of a theorem of this sort is the Hahn–Banach theorem. Every compact metric space (or metrizable space) is...

as a special case. A Banach space Y is said to have the Radon–Nikodym property if the generalization of the Radon–Nikodym theorem also holds, mutatis mutandis...

are disjoint. The hyperplane separation theorem is due to Hermann Minkowski. The Hahn–Banach separation theorem generalizes the result to topological vector...