[Settfa] Tuesday 11/02, Richard Lechner

[kubis at math.cas.cz]

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 Tuesday 11th February, 10:00am 
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 Speaker:Richard Lechner, Institute of Analysis
Johannes Kepler University Linz
 Title: Factorization of the identity operator

 Abstract  

 The origin of our factorization problems is the 1960 paper ``Projections in certain Banach spaces'' by Pe{\l}czy{\'n}ski, where he proved that the spaces $\ell^p$, $1\leq p < \infty$ are prime. Since then, a great number of papers contributing to the understanding of Banach spaces appeared. The most significant, influential and closely related to our work are
 
(1) \item $\ell^\infty$ is prime: Lindenstrauss 1967, ``On complemented subspaces of $m$'';
 
(2) $L^p$, $1\leq p <\infty$ is primary: Enflo (published by Maurey in 1975), ``Sous-espaces compl\'ement\'es de $L^p$, d'apr\`es P.~Enflo'';
 
(3) the space of bounded analytic functions on the poly-disc is primary: Bourgain 1983, ``On the primarity of $H^{\infty}$-spaces''.
 
We address two basic types of factorization problems: infinite dimensional factorization problems and finite dimensional, quantitative factorization problems in several classical Banach spaces.

 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .