Tuesday 02/06, Marek Cúth

kubis at math.cas.cz kubis at math.cas.cz
Fri May 29 11:00:01 CEST 2020


 Tuesday 2nd June, 10:00am 
  Place: IM in Blue lecture hall (Modrá posluchárna)


 Speaker:Marek Cúth, Charles University
 Title: The complexity of isometry classes of Banach spaces


 I will present our recent joint work with M. Doucha, M.
Doležal and O. Kurka (seehttps://arxiv.org/
994), where we
develop a new natural topological approach to coding of separable Banach
spaces. It makes meaningful questions such as which Banach spaces are
the easiest to define, up to isometry (and also up to isomorphism), or
which classes of Banach spaces are the easiest to define - in the
descriptive set theoretic framework. These questions are in turn related
to several conjectures on linear/nonlinear geometry of Banach spaces.
The paper is inspired by the recent paper "G. Godefroy and J.
Saint-Raymond, Descriptive complexity of some isomorphism classes of
Banach spaces, J. Funct. Anal., 275 (2018), pp. 1008–1022", however, it
goes quite further and thoroughly compares ours and theirs approaches.
Among the results, there are new characterizations of the separable
infinite-dimensional Hilbert space as the separable infinite-dimensional
Banach space whose both isometry and isomorphism classes are the easiest
to define among Banach spaces (such statements are made absolutely
precise). We also precisely characterize the complexity of the isometry
classes of the most classical Banach spaces such as L_p[0,1], l_p, for
finite 1<=p, c_0, and also of the Gurarii space. The paper opens a new
area for research and a we suggest several open problems.

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

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