Tuesday 23/01, Noé de Rancourt

[kubis at math.cas.cz]

 ------------------------------------------------------------------------- 

 Tuesday 23rd January, 10:00am 
 ------------------------------------------------------------------------- 

 Speaker:Noé de Rancourt, Université Paris Diderot - Paris 7
 Title: A dichotomy for spaces non-isomorphic to $\ell_2$

 Abstract  

In 1996, in order to solve the homogeneous space problem,
asking if every Banach space which is isomorphic to all of its closed
infinite dimensional subspaces must be isomorphic to $\ell_2$, Gowers
proved his celebrated dichotomy between spaces with an unconditional basis
and hereditarily indecomposable spaces. In this talk, I will present a
variation of this dichotomy ensuring that the subspace it provides is not
isomorphic to $\ell_2$; this result could help to solve a question asked
by V. Ferenczi and C. Rosendal about the number of pairwise non-isomorphic
subspaces of a separable Banach space. This is a joint work with Valentin
Ferenczi. I will then present the combinatorial methods used in the proof
of this dichotomy, by introducing a general Ramsey result generalizing at
the same time Galvin-Prikry's theorem and Gowers' Ramsey-type theorem for
block-sequences.


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