Rosenthal's l^1-Theorem ( II / III )

Datum

19.01.2016

Zeit

14:50 - 15:50

Sprecher

Jun.-Prof. Dr. Martin Schneider

Zugehörigkeit

TU Dresden, Institut für Algebra

Sprache

en

Hauptthema

Mathematik

Andere Themen

Mathematik

Host

Prof. Dr. A. Thom / Dr. T. Netzer

Beschreibung

This series of lectures aims at Master‘s and PhD students in mathematics and offers a first glimpse into topics which are not routinely taught in our MSc/PhD programme. The emphasis is to introduce new concepts and techniques, and not to present full mathematical details. Abstract: Rosenthal’s l^1-theorem states that any bounded sequence in a Banach space that does not contain a weakly Cauchy subsequence admits a subsequence being equivalent to the unit vector base of l^1. In particular, this means that every Banach space either contains a copy of l^1 or has the property that every bounded sequence admits a weakly Cauchy subsequence. Although the statement of Rosenthal's theorem requires just very little background in functional analysis, its proof is complicated and relies on deep results from Ramsey theory. The aim of the course will be to give a sketch of the proof and (if time permits) to discuss some applications, such as the Josefson-Nissenzweig theorem.

Links

• Graduate Lectures in Mathematics
• Poster mit allen Terminen

Letztmalig verändert: 18.12.2015, 14:40:13