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...

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...

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

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

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...

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

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

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

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

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

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}...

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...

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

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...

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

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...

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...

\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...

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

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...

mathematics, the Goldstine theorem, named after Herman Goldstine, is stated as follows: Goldstine theorem. Let X {\displaystyle X} be a Banach space, then the image...

normed space has an extreme point. Furthermore, SKM together with the Hahn–Banach theorem for real vector spaces (HB) are also equivalent to the axiom of choice...

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

\prime }} called evaluation map, that is linear. It follows from the Hahn–Banach theorem that J {\displaystyle J} is injective and preserves norms:  for all ...

{\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])}...

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...

selection theorem concerning the convergence of sequences of functions, Helly published a proof of a special case of the Hahn–Banach theorem, 15 years...