Previous talks this semester:
21.11, 28.11 - Piotr Koszmider, On certain Banach space
In my talk I willl present some random version of the split interval K and will describe some properities
of the Banach space C(K). It is the space of the paper
"P. Koszmider, On a problem of Rolewicz about Banach spaces that admit support sets; J. Funct. Anal. 257 (2009), no. 9, 2723–2741.
I hope the anti-Ramsey theoretic properties of the space can be exploited much more.
24.10, 31.10 - Przemysław Ohrysko, On the Arens - Royden theorem. This theorem implies that the space of
multiplicative funtionals on M(T) with the weak* topology is not homeomorphic to βN.
The participants should revise the following topics before the talks:
- Banach algebras, spectrum and spectral radius.
- Gelfand theory, Gelfand transform, semisimplicity, multiplicative linear functionals, functional calculus.
- Information about structure of the group of invertible elements as in book "Banach algebras" by W. Zelazko or in book "Functional Analysis" by W. Rudin.
- Additional definitions and theorems related to them:
- join spectrum of elements in commutative Banach algebras.
- multivariable functional calculus.
- Shilov idempotent theorem.
10.10.2013 and 17.10.2013. at 1pm, room 106
Tomasz Kochanek, Twisted sums with C(K)-spaces
Based on F. Cabello Sanchez, J.M.F. Castillo, N.J. Kalton, D.T. Yost, Twisted sums with C(K) spaces, TAMS 355 (2003), 4523-4541;
3.10.2013. at 1pm, room 106
Cristóbal Rodriguez (Paris 7);
The Open Coloring Axiom and embeddings into P(N)/fin.
Abstract; The Open Coloring Axiom (OCA), as introduced by Todorcevic in
1989, is a combinatorial principle that has been very successful in
answering questions related to the automorphism group of P(N)/fin, and
has found applications in other structures such as C*-algebras. In this
session we intend to introduce the axiom, showing some easy applications
and stating some important consequences, and then we will go on to show
a more elaborate use of the principle by sketching the proof of the
following theorem by Todorcevic: If I is a nonatomic analytic ideal on
N, then P(N)/I is not isomorphic to a subalgebra of P(N)/fin.
Talks in the second semester of 2012-13.
Talks in the first semester of 2012-13.
Talks in the second semester of 2011-12.
Talks in the first semester of 2011-12.