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  5. Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.31 (2000) s1
  6. Lectures on Rosenthal's l^1-theorem
 
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Lectures on Rosenthal's l^1-theorem

Behrends, Ehrhard
2000
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ISSN
0049-4704
http://hdl.handle.net/10077/4308
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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, ... ).
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
31 (2000) suppl.1
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.
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