Please use this identifier to cite or link to this item: 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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