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...

the Banach–Steinhaus theorem, the Banach–Mazur game, the Banach–Alaoglu theorem, and the Banach fixed-point theorem. Stefan Banach was born on 30 March...

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

{\displaystyle X,} are continuous. Its importance comes from the Banach–Alaoglu theorem. Banach–Alaoglu theorem—Let X {\displaystyle X} be a normed vector space. Then...

unit ball in the dual of a normed space, also known as the Banach–Alaoglu theorem. Alaoglu was born in Red Deer, Alberta to Greek parents. He received...

equipped with the w*-topology. This unit ball K is then compact by the Banach–Alaoglu theorem. The embedding j is introduced by saying that for every x ∈ X, the...

this theorem is an important step in deciding which spaces of weak solutions to use in solving a PDE. Banach–Alaoglu theorem Bishop–Phelps theorem Mazur's...

The Delta-compactness theorem is similar to the Banach–Alaoglu theorem for weak convergence but, unlike the Banach-Alaoglu theorem (in the non-separable...

complex Banach spaces. Banach–Alaoglu theorem – Theorem in functional analysis Dual norm – Measurement on a normed vector space Eberlein–Šmulian theorem – Relates...

the Banach–Alaoglu theorem on the weak-* compactness of the unit ball of the dual space of a normed vector space, and the Arzelà–Ascoli theorem characterizing...

out to be locally compact and Hausdorff. (This follows from the Banach–Alaoglu theorem.) The space Φ A {\displaystyle \Phi _{A}} is compact (in the topology...

Fredholm's theorem (linear algebra) Analytic Fredholm theorem (functional analysis) Banach–Alaoglu theorem (functional analysis) Banach–Mazur theorem (functional...

category theorem Open mapping theorem (functional analysis) Closed graph theorem Uniform boundedness principle Arzelà–Ascoli theorem Banach–Alaoglu theorem Measure...

then actually proved by James in 1964. Banach–Alaoglu theorem – Theorem in functional analysis Bishop–Phelps theorem Dual norm – Measurement on a normed...

has an orthonormal basis. The Banach–Alaoglu theorem about compactness of sets of functionals. The Baire category theorem about complete metric spaces...

compact convex set. Both of these results follow immediately from the Banach–Alaoglu theorem. In the unital commutative case, for the C ∗ {\displaystyle C^{*}}...

Tychonoff's theorem, and also to the conjunction of two fundamental results of functional analysis, the Banach–Alaoglu theorem and the Krein–Milman theorem.[citation...

the Banach–Alaoglu theorem, setting τ {\displaystyle \tau } to the Weak-* topology. That 1. implies 2. is an application of the Bipolar theorem. Let...

J(B)\cap U} as desired. Banach–Alaoglu theorem – Theorem in functional analysis Bishop–Phelps theorem Eberlein–Šmulian theorem – Relates three different...

the Boolean prime ideal theorem (BPI), which is equivalent to the Banach–Alaoglu theorem. Conversely, the Krein–Milman theorem KM together with the Boolean...

unit ball is compact by the Banach–Alaoglu theorem. The norm topology is fundamental because it makes B(H) into a Banach space, but it is too strong for...

product topology and Tychonoff's theorem) to be proven in its full generality, is the Banach–Alaoglu theorem which Stefan Banach first established in 1932 by...

\{0,1\}^{I}} is compact. Each of the following versions of the Banach-Alaoglu theorem is equivalent to the ultrafilter lemma: Any equicontinuous set of...

{\displaystyle X^{*}} . An important fact about the weak* topology is the Banach–Alaoglu theorem: if X is normed, then the closed unit ball in X ∗ {\displaystyle...

Banach norm Banach–Alaoglu theorem Banach–Mazur compactum Banach–Mazur game Banach–Mazur theorem Banach–Ruziewicz problem Banach-Saks theorem Banach-Schauder...

y_{k}-x\rVert \to 0} . Banach–Alaoglu theorem – Theorem in functional analysis Bishop–Phelps theorem Eberlein–Šmulian theorem – Relates three different...

John Philoponus Anthemius of Tralles Leonidas Alaoglu (1914–1981) - Known for Banach- Alaoglu theorem. Charalambos D. Aliprantis (1946–2009) - Founder...

:=\sup _{c\in C}\langle c,y\rangle .} Banach–Alaoglu theorem – Theorem in functional analysis Bipolar theorem – Theorem in convex analysis Polar cone – Concepts...

point of this convex. In the setting above it follows from the Banach-Alaoglu theorem that there always exists extremal points in P ( X ) T {\displaystyle...

subset of a separable reflexive Banach space W {\displaystyle W} . In this case the sequential Banach–Alaoglu theorem implies that any bounded sequence...