Sequences and series in Banach spaces
Sequences and series in Banach spaces
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DOI：
10.1007/978-1-4612-5200-9
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发表时间：
1984
期刊：
影响因子：
--
通讯作者：
J. Diestel
中科院分区：
文献类型：
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作者：
J. Diestel
本书给出了巴拿赫空间理论中出现的一些具有一般分析特征的自然问题的答案。我认为，这里提出的太多结果对于活跃的抽象分析师来说是未知的，而这并不应该是这样的。巴拿赫空间理论可以为分析实践者提供很多帮助。不幸的是，推动该理论并使其许多令人惊叹的成就得以实现的一些一般原则是用该领域的技术术语来表述的，因此对于那些不愿意花费大量时间和精力来破译术语的人来说，它是难以理解的。考虑到这一点，我集中精力呈现我认为任何分析师都可以欣赏、享受甚至可能使用的巴纳赫空间中的基本现象。所涵盖的主题至少有一个严重的遗漏：美丽而强大的类型和共类型理论。坦率地说，如果不增加至少 75% 的文本长度，我就无法说出我想说的关于这个主题的内容。即便如此，这些文字的作用也不如建议去寻找丰富的莫里·施瓦茨研讨会的讲稿，其中该理论的发展可以从其概念中追溯到。同样，Lindenstrauss 和 Tzafriri 的珍贵著作也介绍了类型和共类型的大部分理论，对于那些真正对巴拿赫空间理论感兴趣的人来说，这是必读的。
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's development can be traced from its conception. Again, the treasured volumes of Lindenstrauss and Tzafriri also present much of the theory of type and cotype and are must reading for those really interested in Banach space theory.