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Uniform boundedness principle - Uniform boundedness principle
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Uniform boundedness principle, Uniform boundedness principle - Generalization, Uniform boundedness principle - Uniform boundedness principle, barrelled space, a topological vector space with minimum requirements for the Banach Steinhaus theorem to hold

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Uniform boundedness principle - Uniform boundedness principle: Encyclopedia II - Uniform boundedness principle - Uniform boundedness principle

More precisely, let X be a Banach space and N be a normed vector space. Suppose that F is a collection of continuous linear operators from X to N. The uniform boundedness principle states that if for all x in X we have then Using the Baire category theorem, we have the following short proof: ...

The natural setting for the uniform boundedness principle is a barrelled space where the following generalized version of the theorem holds: Given a barrelled space X and a locally convex space Y, then any family of pointwise bounded continuous linear mappings from X to Y is equicontinuous (even uniformly equicontinuous). ...

Uniform boundedness principle - Uniform boundedness principle

A Wisdom Archive on Uniform boundedness principle - Uniform boundedness principle

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