| Köthe-Bochner Function Spaces Softcover Repri Edition Contributor(s): Lin, Pei-Kee (Author) |
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ISBN: 1461264820 ISBN-13: 9781461264828 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Paperback - Other Formats Published: October 2012 |
| Additional Information |
| BISAC Categories: - Mathematics | Transformations - Mathematics | Functional Analysis - Mathematics | Mathematical Analysis |
| Dewey: 515.732 |
| Physical Information: 0.8" H x 6.14" W x 9.21" (1.19 lbs) 370 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. Randrianantoanina's theorem that property (V*) is a separably determined property, and Odell-Schlumprecht's theorem that every separable reflexive Banach space has an equivalent 2R norm. |