In mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with...

uniform boundedness principle, also known as the Banach–Steinhaus theorem. Important results of functional analysis include: The uniform boundedness principle...

holomorphic, then the limit is also holomorphic. The uniform boundedness principle states that a pointwise bounded family of continuous linear operators between...

boundedness Uniform boundedness principle This disambiguation page lists articles associated with the title Uniform boundedness conjecture. If an internal...

the closed graph theorem, the open mapping theorem, and the uniform boundedness principle. The following notation and notions are used, where R : X ⇉...

operators are closed. Alternatively, it can be argued using the uniform boundedness principle. One relies on the symmetric assumption, therefore the inner...

Every weakly convergent sequence {xn} is bounded, by the uniform boundedness principle. Conversely, every bounded sequence in a Hilbert space admits weakly...

easiest proof uses the non-boundedness of Dirichlet's kernel in L1(T) and the Banach–Steinhaus uniform boundedness principle. As typical for existence...

Hahn–Banach theorem and (independently of Banach and Steinhaus) the uniform boundedness principle. Other theorems include: the Hahn decomposition theorem; the...

continuous T-periodic function need not converge pointwise. The uniform boundedness principle yields a simple non-constructive proof of this fact. In 1922...

the open mapping theorem, the closed graph theorem and the uniform boundedness principle. BCT1 also shows that every nonempty complete metric space with...

graph theorem Uniform boundedness principle Arzelà–Ascoli theorem Banach–Alaoglu theorem Measure of non-compactness Banach–Mazur theorem Bounded linear operator...

dense in X . {\displaystyle X.} A special case of this is the uniform boundedness principle. The empty space is a Baire space. It is the only space that...

operators from X {\displaystyle X} to Y . {\displaystyle Y.} The uniform boundedness principle states that if for all x {\displaystyle x} in X {\displaystyle...

those for which the uniform boundedness principle holds. Every σ ( X ′ , X ) {\displaystyle \sigma \left(X^{\prime },X\right)} -bounded subset of the continuous...

principle can be applied to show that boundedness of f {\displaystyle f} on the region's boundary implies that f {\displaystyle f} is in fact bounded...

of uniform integrability is behind many divergence phenomena for the Fourier series. For example, together with the uniform boundedness principle, it...

Banach algebra, Functional analysis, Banach fixed-point theorem, uniform boundedness principle, Banach–Alaoglu theorem and Banach measure. Lwów School of Mathematics...

(−R, R), then fR converges to f in Lp as R tends to infinity, by the boundedness of the Hilbert transform. Naively one may hope the same holds true for...

theorems imply the boundedness theorem and the extreme value theorem. Rusnock, Paul; Kerr-Lawson, Angus (2005). "Bolzano and Uniform Continuity". Historia...

sup{x**(φ) = φ(x) : x} < ∞, where K is the underlying field. The uniform boundedness principle applies since Hom(X, K) with the norm topology will be a Banach...

Infrabarreled space Uniform boundedness principle#Generalisations – Theorem stating that pointwise boundedness implies uniform boundedness Khaleelulla 1982...

equivalent to one another, and as such, by an argument using the uniform boundedness principle, for any particular p ∈ ( 1 , ∞ ) {\displaystyle p\in (1,\infty...

agency Publication Pueblo Memorial Airport, in Colorado, US The principle of uniform boundedness, in mathematics Pub rock (disambiguation) Public (disambiguation)...

operator, usually defined on a dense subspace. uniform boundedness principle The uniform boundedness principle states: given a set of operators between Banach...

elementary general functional analysis (Hahn–Banach theorem, uniform boundedness principle, Riesz-Kakutani theorem etc.). However, the theory of locally...

Helly's selection theorem (also called the Helly selection principle) states that a uniformly bounded sequence of monotone real functions admits a convergent...

quasi-barrelled space Infrabarreled space Ultrabarrelled space Uniform boundedness principle#Generalisations Khaleelulla 1982, pp. 65–76. Bourbaki, Nicolas...

be a totally bounded sequence and chose a countable dense subset w m {\displaystyle w_{m}} of G {\displaystyle G} . By locally boundedness and a "diagonal...

convex bounded closed set is weakly compact. As a consequence of the principle of uniform boundedness, every weakly convergent sequence is bounded. The...