Köthe-Bochner Function Spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2004
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XIII, 370 p) |
| ISBN: | 9780817681883 9781461264828 |
| DOI: | 10.1007/978-0-8176-8188-3 |
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| 245 | 1 | 0 | |a Köthe-Bochner Function Spaces |c by Pei-Kee Lin |
| 264 | 1 | |a Boston, MA |b Birkhäuser Boston |c 2004 | |
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| 500 | |a 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 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 4 | |a Harmonic analysis | |
| 650 | 4 | |a Functional analysis | |
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| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Functional Analysis | |
| 650 | 4 | |a Analysis | |
| 650 | 4 | |a Abstract Harmonic Analysis | |
| 650 | 4 | |a Operator Theory | |
| 650 | 4 | |a Real Functions | |
| 650 | 4 | |a Probability Theory and Stochastic Processes | |
| 650 | 4 | |a Mathematik | |
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Datensatz im Suchindex
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| author | Lin, Pei-Kee |
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| building | Verbundindex |
| bvnumber | BV042419200 |
| classification_tum | MAT 000 |
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| ctrlnum | (OCoLC)724692374 (DE-599)BVBBV042419200 |
| dewey-full | 515.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-0-8176-8188-3 |
| format | Electronic eBook |
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| id | DE-604.BV042419200 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9780817681883 9781461264828 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027854617 |
| oclc_num | 724692374 |
| open_access_boolean | |
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| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XIII, 370 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Birkhäuser Boston |
| record_format | marc |
| spelling | Lin, Pei-Kee Verfasser aut Köthe-Bochner Function Spaces by Pei-Kee Lin Boston, MA Birkhäuser Boston 2004 1 Online-Ressource (XIII, 370 p) txt rdacontent c rdamedia cr rdacarrier 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 Mathematics Global analysis (Mathematics) Harmonic analysis Functional analysis Operator theory Distribution (Probability theory) Functional Analysis Analysis Abstract Harmonic Analysis Operator Theory Real Functions Probability Theory and Stochastic Processes Mathematik https://doi.org/10.1007/978-0-8176-8188-3 Verlag Volltext |
| spellingShingle | Lin, Pei-Kee Köthe-Bochner Function Spaces Mathematics Global analysis (Mathematics) Harmonic analysis Functional analysis Operator theory Distribution (Probability theory) Functional Analysis Analysis Abstract Harmonic Analysis Operator Theory Real Functions Probability Theory and Stochastic Processes Mathematik |
| title | Köthe-Bochner Function Spaces |
| title_auth | Köthe-Bochner Function Spaces |
| title_exact_search | Köthe-Bochner Function Spaces |
| title_full | Köthe-Bochner Function Spaces by Pei-Kee Lin |
| title_fullStr | Köthe-Bochner Function Spaces by Pei-Kee Lin |
| title_full_unstemmed | Köthe-Bochner Function Spaces by Pei-Kee Lin |
| title_short | Köthe-Bochner Function Spaces |
| title_sort | kothe bochner function spaces |
| topic | Mathematics Global analysis (Mathematics) Harmonic analysis Functional analysis Operator theory Distribution (Probability theory) Functional Analysis Analysis Abstract Harmonic Analysis Operator Theory Real Functions Probability Theory and Stochastic Processes Mathematik |
| topic_facet | Mathematics Global analysis (Mathematics) Harmonic analysis Functional analysis Operator theory Distribution (Probability theory) Functional Analysis Analysis Abstract Harmonic Analysis Operator Theory Real Functions Probability Theory and Stochastic Processes Mathematik |
| url | https://doi.org/10.1007/978-0-8176-8188-3 |
| work_keys_str_mv | AT linpeikee kothebochnerfunctionspaces |