Tomasz Kochanek: Rosenthal’s lemma and its applications

Seminar: Working group in applications of set theory, IMPAN

Thursday, 10.01.2019, 10:15, room 105, IMPAN

Speaker: Tomasz Kochanek (IMPAN/UW)

Title: “Rosenthal’s lemma and its applications ”

Abstact: “In this instructional talk we will recall Rosenthal’s lemma on uniformly bounded sequences of measures and present its several classical applications in the Banach space and vector measures theory. First, we will prove the surprising Nikodym’s uniform boundedness principle and Phillips’ lemma where the application of Rosenthal’s result makes the proofs much easier than the original ones. A few further corollaries of Nikodym’s principle will be mentioned, such as the Dieudonné-Grothendieck theorem on bounded vector measures and the Seever theorem on the range of an operator into a B(Σ)-space. Next, we shall prove two beautiful consequences of Rosenthal’s lemma: the Diestel-Faires theorem and the Orlicz-Pettis theorem. If time allows, we will also briefly discuss their further deep consequences in the structural theory of Banach spaces”.

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