19. 01. 2012.

Marcin Sabok: Automatic continuity for U(l²).

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,w₁])

Based on T. Kania, N. J. Laustsen; Uniqueness of the maximal ideal of the Banach algebra of bounded operators on C([0, w₁])

05. 01. 2012.

Tomasz Kania (University of Lancaster)
On classical operator ideals and the structure of the operator algebra on C([0,w₁])

Based on T. Kania, N. J. Laustsen; Uniqueness of the maximal ideal of the Banach algebra of bounded operators on C([0, w₁])

15. 12. 2011.

Henryk Michalewski: Sets of uniqueness. Continuation. On a theorem of Piatetski-Shapiro

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 l-infty/c-zero; Journal of Mathematical Analysis and Applications 384, 2011, pp. 246-251.

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 k-dimensional space by sets from the the sigma-field generated by the k-dimensional 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 l-infty/c-zero;

27. 10. 2011.

Piotr Koszmider: Going through the paper of S. Todorcevic I; Embedding function spaces into l-infty/c-zero; Journal of Mathematical Analysis and Applications 384, 2011, pp. 246-251.

In this paper descriptive set-theoretic arguments allow the author to link the degree of non-universality of the Banach space l-infty/c_0 with an old combinatorial problem of S. Ulam on sigma-algebras 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 l-infty/c-zero 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 l-infty/c-zero. Previous results used forcing and did not catch a wider combinatorial context of the non-universality of l-infty/c-zero.