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Titlebook: Convergence Structures and Applications to Functional Analysis; R. Beattie,H.-P. Butzmann Book 2002 Springer Science+Business Media Dordre

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发表于 2025-3-21 18:19:21 | 显示全部楼层 |阅读模式
书目名称Convergence Structures and Applications to Functional Analysis
编辑R. Beattie,H.-P. Butzmann
视频videohttp://file.papertrans.cn/238/237736/237736.mp4
图书封面Titlebook: Convergence Structures and Applications to Functional Analysis;  R. Beattie,H.-P. Butzmann Book 2002 Springer Science+Business Media Dordre
出版日期Book 2002
关键词Vector space; function space; functional analysis; topological group; topology
版次1
doihttps://doi.org/10.1007/978-94-015-9942-9
isbn_softcover978-90-481-5994-9
isbn_ebook978-94-015-9942-9
copyrightSpringer Science+Business Media Dordrecht 2002
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发表于 2025-3-21 22:25:29 | 显示全部楼层
Uniform convergence spaces,e convergence generalization of uniform spaces, are not as strong as their topological counterparts. In particular uniform continuity is not a very strong property. But basically all properties of completeness can be carried over to uniform convergence spaces and equicontinuity is an even stronger c
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Hahn-Banach extension theorems,or subspace of . with the property that . ∩.. is closed in each .. - such a subspace is called stepwise closed. Further, let φ bea sequentially continuous linear functional on .. Does there exist a (sequentially) continuous linear extension to .? This is a difficult and much researched problem. Subs
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The Banach-Steinhaus theorem,are locally convex topological vector spaces and . is barrelled, then every pointwise bounded subset of ?. is equicontinuous. This powerful theorem is used, for example to show that the pointwise limit of a sequence of continuous linear mappings is a continuous linear mapping. It is used as well to
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Duality theory for convergence groups,ter group, i.e., the character group of its character group. Here each character group carries the compact-open topology. There are various generalizations of this result to not necessarily locally compact, commutative topological groups. Probably the first one was due to S. Kaplan who generalized t
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