Tuesday 02/06, Marek Cúth

[kubis at math.cas.cz]

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

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

 Abstract  

 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 .