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

In mathematics, a uniformly bounded family of functions is a family of bounded functions that can all be bounded by the same constant. This constant is...

algebraic geometry and number theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian varieties states that the...

Uniform boundedness conjecture may refer to: Uniform boundedness conjecture for torsion points Uniform boundedness conjecture for rational points Uniform...

operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm. The...

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

in PN(K), and the general Uniform Boundedness Conjecture says that the number of preperiodic points in PN(K) may be bounded solely in terms of N, the...

In arithmetic geometry, the uniform boundedness conjecture for rational points asserts that for a given number field K {\displaystyle K} and a positive...

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

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

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

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

Ultrabarrelled space Uniform boundedness principle#Generalisations – Theorem stating that pointwise boundedness implies uniform boundedness Ursescu theorem –...

under f {\displaystyle f} is bounded. The following theorem relates local boundedness of functions with the local boundedness of topological vector spaces:...

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

normability criterion – Characterization of normable spaces Local boundedness Totally bounded space – Generalization of compactness Narici & Beckenstein 2011...

d\mu }=\int _{S}{f\,d\mu }.} Remark: The pointwise convergence and uniform boundedness of the sequence can be relaxed to hold only μ-almost everywhere,...

satisfied by a uniformly bounded sequence { fn } of differentiable functions with uniformly bounded derivatives. Indeed, uniform boundedness of the derivatives...

a bounded set in Y {\displaystyle Y} .[citation needed] Weaker than boundedness is local boundedness. A family of bounded functions may be uniformly bounded...

of rational maps, and her recent proof (with DeMarco and Ye) of uniform boundedness results for numbers of torsion points on families of bielliptic genus...

implies χ ( R / P , R / Q ) > 0 {\displaystyle \chi (R/P,R/Q)>0} . Uniform boundedness conjecture for rational points: do algebraic curves of genus g ≥...

In mathematics, uniform integrability is an important concept in real analysis, functional analysis and measure theory, and plays a vital role in the...

Patricia Pacelli showed that the Bombieri–Lang conjecture implies a uniform boundedness conjecture for rational points: there is a constant B g , d {\displaystyle...

is 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...

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

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

mathematics, total-boundedness is a generalization of compactness for circumstances in which a set is not necessarily closed. A totally bounded set can be covered...

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

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

(Zhu 2007, Theorem 1.14, p.11), and note in this reference that the uniform boundedness will apply in the situation where F ⊆ X satisfies (∀φ ∈ Hom(X, K))...