[Settfa] SPECIAL SEMINAR THIS FRIDAY

[Wieslaw Kubis (gmail)]

Dear Colleagues,

There was no seminar this Tuesday, however there will be a special 
seminar this Friday 21.10.2016, 10:00, seminar room Konirna (Zitna 25, 
Praha 1). There will be two talks, the details are below.

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TALK #1: Szymon Draga (University of Silesia in Katowice, Poland)
TITLE:  The Szlenk power type of non-separable Banach spaces

ABSTRACT: We will show that summability of the Szlenk index as well as 
the Szlenk power type are separably determined. We will give some 
applications to direct sums and injective tensor products.

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TALK #2: Tomasz Kania (University of Warwick, UK)
TITLE: Steinhaus' lattice-point problem for Banach spaces

ABSTRACT: Steinhaus proved that given a positive integer $n$, one may 
find a circle surrounding exactly $n$ points of the integer lattice. 
This statement has been recently extended to Hilbert spaces where the 
integer lattice was replaced by any infinite set that intersects every 
ball in at most finitely many points. We investigate Banach spaces 
satisfying this property, which we call (S), and we characterise them by 
means of a new geometric property of the unit sphere which allows us to 
show, e.g., that all strictly convex norms have (S), nonetheless, there 
are plenty of non-strictly convex norms satisfying (S). We also study 
the corresponding renorming problem. Assuming that the Lebesgue measure 
can be extended to a measure defined on the power set of the reals, we 
construct a Banach space that has (S) but it does not have a strictly 
convex renorming.
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