bio | website | maths.lancs.ac.uk/~kania |
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location | Warsaw / Lancaster | |
age | ||
visits | member for | 3 years, 4 months |
seen | 17 hours ago | |
stats | profile views | 1,604 |
Sep 14 |
comment |
Ultrapowers of Banach spaces without the continuum hypothesis
If CH fails, then you can find $2^{\mathfrak{c}}$ ultrapowers of $C(K)$ which are not isometric to $\ell_\infty / c_0$. As for the isomorphic case, it seems that there are also $2^{\mathfrak{c}}$ isomorphic types by a version of Theorem 3 from arxiv.org/pdf/0912.0406.pdf adjusted to the setting of ptmat.fc.ul.pt/~alexus/papers/unstable.pdf |
Sep 11 |
comment |
Reference request for sums of Grothendieck spaces
For $p\in (1,\infty)$ the proof (of this exercise) can be found in eweb.unex.es/eweb/extracta/Vol-18-3/18J3Plich.pdf (Lemma 1). |
Sep 7 |
revised |
Chebyshev centres of a bounded closed convex set in a strictly convex Banach space
title improved |
Sep 7 |
comment |
Existence of normal structure in strictly convex Banach spaces
You may consider accepting my answer. |
Sep 7 |
suggested | suggested edit on Chebyshev centres of a bounded closed convex set in a strictly convex Banach space |
Sep 6 |
revised |
Operators on $\ell_\infty(\Gamma)$ and almost disjoint families of subsets
dr |
Sep 6 |
revised |
Operators on $\ell_\infty(\Gamma)$ and almost disjoint families of subsets
answer |
Sep 6 |
revised |
Operators on $\ell_\infty(\Gamma)$ and almost disjoint families of subsets
dr |
Sep 6 |
answered | Operators on $\ell_\infty(\Gamma)$ and almost disjoint families of subsets |
Sep 1 |
comment |
Ultracoproducts and Cartesian products
Just to complement your answer, my remark actually covers Ghasemi's result as SAW*-algebras are Grothendieck. However, one can easily prove that $K=(X\times Y)^U$ is an F-space in which case $C(K)$ is a Grothendieck space; in other words no C*-machinery is required here. |
Aug 30 |
revised |
Erdős cardinals and ineffable cardinals
sorry, I had to |
Aug 30 |
suggested | suggested edit on Erdős cardinals and ineffable cardinals |
Aug 25 |
comment |
Is the absolute of a compact space the projective limit of the Stone-Čech compactifications of its open dense subsets?
There is also a related result: A. Błaszczyk, A construction of a Gleason spaces, Commentationes Mathematicae Universitatis Carolinae 24 (1983), 233-236. It gives a description of the projective cover as the Stone-Čech compactification of the strongest topology subject to the condition that the identity map is irreducible. |
Aug 23 |
revised |
Jonsson Boolean algebras?
typos |
Aug 20 |
revised |
Ultracoproducts and Cartesian products
this is what I meant |
Aug 20 |
revised |
Ultracoproducts and Cartesian products
more |
Aug 20 |
revised |
Ultracoproducts and Cartesian products
dr |
Aug 20 |
answered | Ultracoproducts and Cartesian products |
Aug 14 |
comment |
Is the ideal of functions vanishing at a set complementable in $C(X)$?
Borsuk assumed that $X$ is separable; Dugundji proved that it is enough to assume that only $Y$ is separable: J. Dugundji, An extension of Tietze's theorem. Pacific Journal of Mathematics 1 (1951), no. 3, 353--367. There are two nice papers, one due to Pełczyński and the second one due to Haydon, about spaces which satisfy the above-mentioned theorem. Google for the term: "Dugundji space". |
Aug 5 |
revised |
The Banach space of bounded functions with countable support
dr |