Hi all,
Please join us for the following talk on Friday, March 24 at 9am (Central Daylight Time). Please use the following link to attend
Join Zoom Meeting https://unt.zoom.us/j/84342187681
Best regards,
Bunyamin https://researchseminars.org/seminar/BanachWebinars researchseminars.org - View series https://researchseminars.org/seminar/BanachWebinars Welcome to researchseminars.org, a list of research seminars and conferences! researchseminars.org
Speaker: Kamil Krzysztof Ryduchowski (Warsaw) Title: Equilateral and separated sets in some nonseparable Banach spaces.
Abstract: A subset S of a Banach space X is called r-equilateral (resp., r-separated) if any two points of S are in the distance exactly r (resp., at least r) from each other. Whereas Terenzi constructed an infinite-dimensional Banach space without infinite equilateral sets, Elton and Odell proved that the unit sphere of every infinite-dimensional Banach space contains an infinite (1+r)-separated set for some r>0. Recently, some research has been done concerning the uncountable versions of these problems, e.g., Kania, Hajek and Russo proved that the unit sphere of every nonseparable reflexive Banach spaces contains an uncountable (1+r)-separated set for some r>0.
During my talk, I will present some known results concerning this line of research and discuss joint results with Piotr Koszmider. In particular, I will show that, under some set-theoretic assumptions, there is an equivalent renorming of the nonseparable Hilbert space ell_2(omega_1) without uncountable equilateral sets.