| 書目名稱 | K?the-Bochner Function Spaces | | 編輯 | Pei-Kee Lin | | 視頻video | http://file.papertrans.cn/542/541570/541570.mp4 | | 概述 | Contains recent results of the geometric properties in the K(oe)the-Bochner spaces.Each section is independent of each other, allowing the different levels of readership | | 圖書封面 |  | | 描述 | This monograph isdevoted to a special area ofBanach space theory-the Kothe- Bochner function space. Two typical questions in this area are: Question 1. Let E be a Kothe function space and X a Banach space. Does the Kothe-Bochner function space E(X) have the Dunford-Pettis property if both E and X have the same property? If the answer is negative, can we find some extra conditions on E and (or) X such that E(X) has the Dunford-Pettis property? Question 2. Let 1~ p~ 00, E a Kothe function space, and X a Banach space. Does either E or X contain an lp-sequence ifthe Kothe-Bochner function space E(X) has an lp-sequence? To solve the above two questions will not only give us a better understanding of the structure of the Kothe-Bochner function spaces but it will also develop some useful techniques that can be applied to other fields, such as harmonic analysis, probability theory, and operator theory. Let us outline the contents of the book. In the first two chapters we provide some some basic results forthose students who do not have any background in Banach space theory. We present proofs of Rosenthal‘s l1-theorem, James‘s theorem (when X is separable), Kolmos‘s theorem, N. Randriananto | | 出版日期 | Book 2004 | | 關(guān)鍵詞 | Banach Space; Convexity; Martingale; Operator theory; Smooth function; continuous function; functional ana | | 版次 | 1 | | doi | https://doi.org/10.1007/978-0-8176-8188-3 | | isbn_softcover | 978-1-4612-6482-8 | | isbn_ebook | 978-0-8176-8188-3 | | copyright | Springer Science+Business Media New York 2004 |
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