Uniform boundedness principle
In mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem, it is considered one of the cornerstones of the field. In its basic form, it asserts that for a family of continuous linear operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm.
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Uniform boundedness principle
In mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem, it is considered one of the cornerstones of the field. In its basic form, it asserts that for a family of continuous linear operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm.
has abstract
Banachova-Steinhausova věta ne ...... h operátorů z do . Potom platí
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Der Satz von Banach-Steinhaus ...... tlichen 1912 bei Eduard Helly.
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Em matemática, o teorema de Ba ...... nach e Hugo Steinhaus em 1927.
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En matemàtiques, en l'àrea d'a ...... eorema de categories de Baire.
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In de functionaalanalyse, een ...... heid is die van een tonruimte.
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In matematica, il principio de ...... ezza nella norma operatoriale.
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In mathematics, the uniform bo ...... en independently by Hans Hahn.
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Inom den gren av matematiken s ...... llas ett ofta använt resultat.
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Le théorème de Banach-Steinhau ...... ie comaigre, comme E lui-même.
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Twierdzenie Banacha-Steinhausa ...... tefan Banach i Hugo Steinhaus.
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A.I.
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b/b015200
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math statement
Any weakly bounded subset S in a normed space Y is bounded.
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Given a barrelled space X and ...... d Y is a locally convex space.
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If a sequence of bounded opera ...... s define a bounded operator T.
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Let X be a Banach space and Y ...... to Y. If
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for all , then
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Let X be a Banach space, a se ...... dual set, and thus dense in X.
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Let X be a Fréchet space, Y a ...... he family H is equicontinuous.
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Corollary
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Theorem
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Uniform Boundedness Principle
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Proof
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Banachova-Steinhausova věta ne ...... h operátorů z do . Potom platí
@cs
Der Satz von Banach-Steinhaus ...... ze als Eckpfeiler des Gebiets.
@de
Em matemática, o teorema de Ba ...... nach e Hugo Steinhaus em 1927.
@pt
En matemàtiques, en l'àrea d'a ...... eorema de categories de Baire.
@ca
In de functionaalanalyse, een ...... grensdheid in de operatornorm.
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In matematica, il principio de ...... ezza nella norma operatoriale.
@it
In mathematics, the uniform bo ...... boundedness in operator norm.
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Inom den gren av matematiken s ...... llas ett ofta använt resultat.
@sv
Le théorème de Banach-Steinhau ...... ie comaigre, comme E lui-même.
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Twierdzenie Banacha-Steinhausa ...... tefan Banach i Hugo Steinhaus.
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label
Banach-Steinhaus sats
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Banachova–Steinhausova věta
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Principe van uniforme begrensdheid
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Principio dell'uniforme limitatezza
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Satz von Banach-Steinhaus
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Teorema de Banach-Steinhaus
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Teorema de Banach-Steinhaus
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Théorème de Banach-Steinhaus
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Twierdzenie Banacha-Steinhausa
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Uniform boundedness principle
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