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bio website maths.lancs.ac.uk/~kania
location Warsaw / Lancaster
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visits member for 3 years, 4 months
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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