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Uniform boundedness principle - Generalization | | Uniform boundedness principle - Generalization: Encyclopedia II - Uniform boundedness principle - Generalization | | 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).
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See also:Uniform boundedness principle, Uniform boundedness principle - Uniform boundedness principle, Uniform boundedness principle - Generalization | | | 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 | | |
| | | Uniform boundedness principle: Encyclopedia II - Uniform boundedness principle - Generalization
Uniform boundedness principle - Generalization
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).
Other related archives1927, Baire category theorem, Baire space, Banach space, Hahn-Banach theorem, Hans Hahn, Hugo Steinhaus, Stefan Banach, barrelled space, continuous linear mappings, continuous linear operators, equicontinuous, functional analysis, locally convex space, mathematics, normed vector space, open mapping theorem, topological vector space, uniformly equicontinuous
 Adapted from the Wikipedia article "Generalization", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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