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http://hdl.handle.net/10077/4308
Title: | Lectures on Rosenthal's l^1-theorem | Authors: | Behrends, Ehrhard | Issue Date: | 2000 | Publisher: | Università degli Studi di Trieste. Dipartimento di Scienze Matematiche | Source: | Ehrhard Behrends, "Lectures on Rosenthal's l^1-theorem", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 31 (2000) suppl.1, pp. 71-106. | Series/Report no.: | Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics 31 (2000) suppl.1 |
Abstract: | Let $x\left(n\right)$ be a bounded sequence in a Banach space X. Rosenthal's $l^{1}$-theorem states that there is essentially only one exceptional situation where it is $\mathit{not}$ possible to extract a subsequence which is a weak Cauchy sequence: This happens if (x$_{n}$) is the sequence of unit vectors in $l^{1}$.The aim of these lectures is twofold: On the one hand results from the last few years centering around this theorem are presented, and on the other hand the opportunity is taken to introduce the audience to a number of techniques which are of importance in modern Banach space theory (Ramsey theory, Martin's axiom, ... ). |
Type: | Article | URI: | http://hdl.handle.net/10077/4308 | ISSN: | 0049-4704 |
Appears in Collections: | Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.31 (2000) s1 |
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File | Description | Size | Format | |
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BehrendsRendMat31s1.pdf | 373.3 kB | Adobe PDF | ![]() View/Open |
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