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Lectures on Rosenthal's l^1-theorem
Behrends, Ehrhard
2000
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.
Languages
en
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