List of the talks:
19. 01. 2012.
Marcin Sabok:
Automatic continuity for U(l^{2}).
We will discuss a recent paper of Tsankov, which proves that
the group of unitary operators on the infinite dimensional separable
Hilbert space has the automatic continuity property. This means that
arbitrary algebraic homomorphism from this group into a separable
group is continuous. Automatic continuity
property has many interesting consequences, for example, it implies
uniqueness of a Polish group topology on the group if such topology
exists.
Based on T. Tsankov;
Automatic continuity for the unitary group
12. 01. 2012.
Tomasz Kania (University of Lancaster)
On classical operator ideals and the structure of the operator algebra on C([0,w_{1}])
Based on
T. Kania, N. J. Laustsen; Uniqueness of the maximal ideal of the Banach algebra of bounded operators on C([0, w_{1}])
05. 01. 2012.
Tomasz Kania (University of Lancaster)
On classical operator ideals and the structure of the operator algebra on C([0,w_{1}])
Based on
T. Kania, N. J. Laustsen; Uniqueness of the maximal ideal of the Banach algebra of bounded operators on C([0, w_{1}])
15. 12. 2011.
Henryk Michalewski: Sets of uniqueness. Continuation. On a theorem of PiatetskiShapiro
01. 12. 2011.
Henryk Michalewski: Sets of uniqueness. Continuation. See
notes
24. 11. 2011.
Henryk Michalewski: Sets of uniqueness. See
abstract in Polish and German
10. 11. 2011.
Piotr Koszmider: Consistency results related to the rectangle problem and the paper
S. Todorcevic I; Embedding function spaces into linfty/czero;
Journal of Mathematical Analysis and Applications
384, 2011, pp. 246251.
We will prove (following the thesis of K. Kunen) the consistency of the negative
solution to the rectangle problem as well as of the results concerning the impossibility of separating certain
sets in the kdimensional space by sets from the the sigmafield generated by the kdimensional boxes.
The proof is by forcing. The partial order used is the standard Cohen forcing.
03. 11. 2011.
Piotr Koszmider: Going through the paper of S. Todorcevic II; Embedding function spaces into linfty/czero;
27. 10. 2011.
Piotr Koszmider: Going through the paper of S. Todorcevic I; Embedding function spaces into linfty/czero;
Journal of Mathematical Analysis and Applications
384, 2011, pp. 246251.
In this paper descriptive settheoretic arguments allow the author to link the degree of nonuniversality
of the Banach space linfty/c_0 with an old combinatorial
problem of S. Ulam on sigmaalgebras generated by rectangles, known by now to be undecidable (a result due to Kunen). Recall that under CH the Boolean algebra P(w)/Fin is
universal among Boolean algebras of sizes not bigger than continuum, and so linfty/czero is a universal Banach space for Banach spaces of density not bigger than continuum. Using the negative solution to Ulam's problem
the author constructs diverse "simple" compact spaces K (first countable, Corson compacts) such that the Banach space
C(K) cannot be embedded (in diverse senses) in the space linfty/czero. Previous results used forcing and did not catch a wider combinatorial context of the nonuniversality of
linfty/czero.
