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bio website maths.lancs.ac.uk/~kania
location Toronto, Canada
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visits member for 2 years, 11 months
seen 10 hours ago

Apr
14
comment Do all $L^{\infty}(\mu)$ spaces have the Grothendieck property?
user46855, you should post that as the answer.
Apr
14
comment Decomposable Banach Spaces
Koszmider proved that consistently you can have an indecomposable $C(K)$-space of density $2^{\mathfrak{c}}=\aleph_2$. There are however certain limitations of the proof so that it is unlikely that it can be generalised to higher cardinals. On large indecomposable Banach spaces; J. Funct. Anal. 264 (2013), no. 8, 1779–1805
Apr
13
awarded  Revival
Mar
29
accepted Introducing a dual space structure
Mar
29
asked Introducing a dual space structure
Mar
19
revised Banach spaces with no reflexive complemented subspaces
a more appropriate link
Mar
15
revised Banach spaces with no reflexive complemented subspaces
banach-spaces tag added
Mar
15
suggested suggested edit on Banach spaces with no reflexive complemented subspaces
Mar
15
comment Banach spaces with no reflexive complemented subspaces
The example with the Schreier space actually shows that a space failing DPP can have no reflexive subspaces at all.
Mar
15
revised Banach spaces with no reflexive complemented subspaces
link
Mar
15
answered Banach spaces with no reflexive complemented subspaces
Mar
15
comment Is the space of trace class operators finitely representable in an $L^1$-space?
On a tangential note, do we know what are the reflexive subspaces of $S_1$? At least do we know if they are super-reflexive?
Mar
15
comment When is it $C(X)$?
To the best of my knowledge Dales et al. are going to publish (rather soon) a survey article on this and related problems. I will keep you posted.
Mar
15
comment When is it $C(X)$?
Yemon, Haydon in his proof uses Pełczyński's decomposition method hence his result is only isomorphic not isometric, so the trick with uniqueness of preduals doesn't work. This situation is analogous to the fact that there exists a Banach-space between apparently very different Banach algebras $\ell_\infty$ and $L_\infty$. I am not sure if the OP is happy with Banach-space isomorphisms, though.
Mar
12
revised Extension of bounded linear operators
typo
Mar
12
revised Extension of bounded linear operators
examples
Mar
12
answered Extension of bounded linear operators
Mar
10
revised States and extremal states of quantum SU(2) and the Podleś sphere
spelling of *Podleś*
Mar
10
suggested suggested edit on States and extremal states of quantum SU(2) and the Podleś sphere
Mar
1
comment Noncommutative geometry and category theory
That is right. In the realm of C*-algebras it is however more natural to work with the so-called strong Morita equivalence introduced by Rieffel (see for instance his paper Morita equivalence for $C^\ast$-algebras and $W^\ast$-algebras).