01.10.2015, 1115 room 105
Speaker: Tomasz Kochanek (IMPAN/UW)
Title: Uncountable sets of unit vectors that are separated by more than 1
Abstract: "Kottman proved that in the unit ball of any infinite-dimensional
Banach space one can find an infinite subset such that the distance between any two distinct elements
is larger than 1. Elton and Odell, employing Ramsey theory, strengthened this result by showing that
it is possible to have all distances at least equal to 1+c for some c>0 depending only on the given space.
Both these results are far-reaching generalizations of the Riesz lemma. We will investigate their
non-separable versions focusing on two results: (1) the analogue of Kottman's theorem is valid for every non-separable reflexive Banach space
(the set from the assertion is then uncountable); (2) the analogue of the Elton-Odell theorem
is valid for every non-separable superreflexive Banach space."
Time and place: Thursdays 11.15-13.00 am, room 105, Sniadeckich 8
The scope of the seminar:
Set-theoretic combinatorial and topological methods in diverse fields of mathematics, with a special emphasis on abstract analysis like
Banach spaces, Banach algebras, C*-algebras, Here we include both the developing of such methods as
forcing, descriptive set theory, Ramsey theory as well as their concrete applications in the fields mentioned above.
Working group style: We will make efforts so that this seminar has
more a working character rather than the presentation style. This means that we encourage long digressions,
discussions, background preparations and participation of everyone.
We would like to immerse ourselves into the details of the mathematical arguments studied.
Also the talks are usualy devoted to research in progress or fascinating results leading to some project not yet resolved.
While ready final results could be presented at other seminars at IM PAN or UW.
Participants this semester so far:
- Saeed Ghasemi (IM PAN)
- Tomek Kochanek (IM PAN/UW)
- Piotr Koszmider (IM PAN)
- Eva Pernecká (IM PAN)
- Roman Pol (UW)
- Adam Skalski (IMPAN)
- Damian Sobota (Ph. D. student IM PAN)
- Michał Świętek (Ph. D. student UJ)
- Piotr Zakrzewski (UW)
Forthcoming talks (approximately):
- 8.10 Saeed Ghasemi, on authomorphisms of corona C*-algebras I;
- 15.10 Eva Pernecka;
- 22.10 No seminar - Scientific Council of IM PAN
- 29.10 Saeed Ghasemi, on authomorphisms of corona C*-algebras II;
- 5.11 Saeed Ghasemi, on authomorphisms of corona C*-algebras III;
- 12.11 Damian Sobota, Nikodym property of von Neumann algebras;
- 19.11 Damian Sobota, Grothendieck property of von Neumann algebras;