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bio website maths.lancs.ac.uk/~kania
location Lancaster, United Kingdom
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visits member for 3 years, 5 months
seen 53 mins ago

1d
revised Convergence on a random graph
spelling of Łuczak
1d
suggested suggested edit on Convergence on a random graph
Oct
18
comment The space of all compact metric spaces with Gromov-Hausdorff distance
Is it at least known that the space of compact metric spaces modulo isometry is separable? This reminds me of a similar result of Pisier asserting that for each $n\geqslant 2$ the space of $n$-dimensional operator spaces, $O_n$, is non-separable. I am wondering if one could embed $O_n$ in your space.
Oct
15
comment Is $L(\ell_2,\ell_2)$ dense in $L(\ell_2,c_0)$?
Hi Michael, we met at HLF two weeks ago. :)
Oct
15
accepted Discrete subsets in the topology of pointwise convergence vs. metrisability
Oct
14
awarded  Nice Question
Oct
13
comment Discrete subsets in the topology of pointwise convergence vs. metrisability
Santi, this is a brilliant answer. I will accept it in two days. Could you please elaborate a bit more on the first sentence of the final paragraph?
Oct
13
revised Discrete subsets in the topology of pointwise convergence vs. metrisability
edited title
Oct
13
comment A Banach space with all Hilbertian subspaces complemeneted
Maybe being $\pi$-Euclidean would be of use for you? See Cor. 8.4 in Projections onto Hilbertian subspaces of Banach spaces by Figiel and Tomczak-Jaegermann.
Oct
13
comment A Banach space with all Hilbertian subspaces complemeneted
Are there any particular properties that you hope for?
Oct
13
asked Discrete subsets in the topology of pointwise convergence vs. metrisability
Oct
11
answered Is there a non-compact Poulsen simplex?
Oct
2
comment Is $\mathbb{Z}^{\omega}$ ever the union of a chain of proper subgroups each isomorphic to $\mathbb{Z}^{\omega}$?
This paper arxiv.org/pdf/math/0508146v6.pdf might be of relevance.
Oct
1
awarded  Excavator
Oct
1
revised Does the dual Banach space $B(\ell^\infty)$ have weak* normal structure?
formating, grammar improved
Oct
1
suggested suggested edit on Does the dual Banach space $B(\ell^\infty)$ have weak* normal structure?
Sep
30
awarded  Explainer
Sep
29
revised Is there any standard procedure to properly define a composite metric?
link added
Sep
29
suggested suggested edit on Is there any standard procedure to properly define a composite metric?
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