October 23rd, Michał Świętek (Ph. D. student UJ/WCMCS-IM PAN) 1115 room 105:
Exotic Banach spaces via Boolean algebras and Stone spaces
Abstract: One of the oldest questions in the theory of Banach spaces was
whether every Banach space is isomorphic to its hyperplanes.
This was answered negatively by Gowers and Mauray.
During my talk I will present a construction of a
classical C(K) space, based on the paper Piotr Koszmider, Banach spaces of continuous functions with few operators.
Math. Ann. 330 (2004), no. 1, 151–183, which also answers the above question negatively.
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.
Participants this semester so far:
- Leandro Candido (IM PAN/USP)
- Marek Cuth (WCMCS-IM PAN)
- Michal Doucha (IMPACT/IM PAN)
- Piotr Koszmider (IM PAN)
- Maciej Malicki (SGH)
- Gabriel Salazar (IM PAN)
- Damian Sobota (Ph. D. student IM PAN)
- Michał Świętek (Ph. D. student UJ/WCMCS-IM PAN)
- Michał Wojciechowski (IM PAN)
- 30.10 - Marek Cuth (WCMCS-IM PAN): The method of elementary submodels can be viewed as a
tool of set theory which enables us to handle very complicated inductive constructions.
I will present how elementary submodels can be used in Banach space theory.
More precisely: in 1993 Argyros and Mercourakis introduced a class of Banach spaces called
weakly Lindelof determined (WLD). It appeared that this class of WLD Banach spaces
has many nice properties and it is possible to find nice characterizations of it.
I will present how elementary submodels
can be used in order to prove some of those characterizations and prove a
characterization of WLD spaces in terms of elementary submodels.