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Titlebook: Sequences and Series in Banach Spaces; Joseph Diestel Textbook 1984 Springer-Verlag New York, Inc. 1984 Banach.Banach Space.Banachscher Ra

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发表于 2025-3-21 20:09:13 | 显示全部楼层 |阅读模式
书目名称Sequences and Series in Banach Spaces
编辑Joseph Diestel
视频video
丛书名称Graduate Texts in Mathematics
图书封面Titlebook: Sequences and Series in Banach Spaces;  Joseph Diestel Textbook 1984 Springer-Verlag New York, Inc. 1984 Banach.Banach Space.Banachscher Ra
描述This volume presents answers to some natural questions of a general analytic character that arise in the theory of Banach spaces. I believe that altogether too many of the results presented herein are unknown to the active abstract analysts, and this is not as it should be. Banach space theory has much to offer the prac­ titioners of analysis; unfortunately, some of the general principles that motivate the theory and make accessible many of its stunning achievements are couched in the technical jargon of the area, thereby making it unapproachable to one unwilling to spend considerable time and effort in deciphering the jargon. With this in mind, I have concentrated on presenting what I believe are basic phenomena in Banach spaces that any analyst can appreciate, enjoy, and perhaps even use. The topics covered have at least one serious omission: the beautiful and powerful theory of type and cotype. To be quite frank, I could not say what I wanted to say about this subject without increasing the length of the text by at least 75 percent. Even then, the words would not have done as much good as the advice to seek out the rich Seminaire Maurey-Schwartz lecture notes, wherein the theory
出版日期Textbook 1984
关键词Banach; Banach Space; Banachscher Raum; Convexity; Sequences; Series; Spaces; choquet integral; compactness;
版次1
doihttps://doi.org/10.1007/978-1-4612-5200-9
isbn_softcover978-1-4612-9734-5
isbn_ebook978-1-4612-5200-9Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer-Verlag New York, Inc. 1984
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发表于 2025-3-21 21:45:35 | 显示全部楼层
https://doi.org/10.1007/978-1-4612-5200-9Banach; Banach Space; Banachscher Raum; Convexity; Sequences; Series; Spaces; choquet integral; compactness;
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978-1-4612-9734-5Springer-Verlag New York, Inc. 1984
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,The Eberlein-Šmulian Theorem,f a Banach space . get to be weakly compact? The two are related. Before investigating their relationship, we look at a couple of necessary ingredients for weak compactness and take a close look at two illustrative nonweakly compact sets.
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The Classical Banach Spaces, of the results treated thus far were first derived in special cases, then understood to hold more generally. Not too surprisingly, along the path to general results many important theorems, special in their domain of applicability, were encountered. In this chapter, we present more than a few such results.
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,An Intermission: Ramsey’s Theorem,whenever . < . holds for each . ∈ . and . ∈ .. The collection of finite subsets of . is denoted by ..(.) and the collection of infinite subsets of . by ..(.). More generally for . ⊆ . we denote by ..(. the colelction { . ∈ .. (.) : . ⊆ .. ∪ ., . < . . } and by .. (.) the collection { . ∈ .. (.): . ⊆ . ⊆ . ∪ ., . < . . }.
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The Josefson-Nissenzweig Theorem,y in .* differ. Can they have the same convergent sequences? The answer is a resounding “no!” and it is the object of the present discussion. More precisely we will prove the following theorem independently discovered by B. Josef son and A. Nissenzweig.
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