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...

(under ZF) to the Banach–Alaoglu theorem, which is another foundational theorem in functional analysis. Although the Banach–Alaoglu theorem implies HB, it...

{\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...

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...

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...

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

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

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...

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...

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

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

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

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

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

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

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

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...

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...

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...

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

\{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...

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

{\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...

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

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...

& Border 2006, p. 230 Rudin 1991, Theorem 3.3 Corollary, p. 59 Rudin 1991, Theorem 3.15 The Banach–Alaoglu theorem algorithm, p. 68 Rudin 1991, p. 94...

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

on the dual of C ( X ) . {\displaystyle {\mathcal {C}}(X).} The Banach–Alaoglu theorem implies that any normed space is isometrically isomorphic to a subspace...