# [Settfa] Tuesday 11/02, Richard Lechner

kubis at math.cas.cz kubis at math.cas.cz
Fri Feb 7 10:00:02 CET 2020

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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 $\ell^p$, $1\leq p &lt; \infty$ 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) $L^p$, $1\leq p &lt;\infty$ 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.

https://calendar.math.cas.cz/set-theory-and-analysis-actual .

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