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bio website maths.lancs.ac.uk/~kania
location Warsaw / Lancaster
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visits member for 2 years, 9 months
seen Jul 26 at 13:55

Jul
23
comment Maximal Ideals and Maximal Subspaces in normed algebras
Thank you Jonas, corrected!
Jul
23
revised Maximal Ideals and Maximal Subspaces in normed algebras
corrected
Jul
23
comment Maximal Ideals and Maximal Subspaces in normed algebras
The map $f \mapsto f(5)$ is linear and multiplicative but $\sup f(5)$, where $f$ has norm one, is infinite.
Jul
23
revised Maximal Ideals and Maximal Subspaces in normed algebras
serious correcrions
Jul
23
awarded  Mortarboard
Jul
23
comment Maximal Ideals and Maximal Subspaces in normed algebras
I gave the example and I will prove it indeed works in the afternoon as now I have to go. It should be also mentioned in Kaniuth's book.
Jul
23
revised Maximal Ideals and Maximal Subspaces in normed algebras
more
Jul
22
comment Maximal Ideals and Maximal Subspaces in normed algebras
Jonas, where do you ask about completeness? I can give a counterexample in the non-complete setting.
Jul
22
revised Maximal Ideals and Maximal Subspaces in normed algebras
-,
Jul
22
comment Maximal Ideals and Maximal Subspaces in normed algebras
I have improved my answer.
Jul
22
revised Maximal Ideals and Maximal Subspaces in normed algebras
more
Jul
17
comment Dual of $l^\infty$ is not $l^1$
Oh, yes, but functional analysis without choice is a nightmare!
Jul
17
answered Dual of $l^\infty$ is not $l^1$
Jul
17
revised Reflexivity of $\ell^p$
I guess that reflexivity is the right term in English
Jul
17
suggested suggested edit on Reflexivity of $\ell^p$
Jul
16
comment If A has positive Haar measure then $AA^{-1}$ is a neighborhood of $e$
math.stackexchange.com/questions/59769/theorem-of-steinhaus
Jul
15
comment Constructing a Banach space of cardinality $\beth_{\omega+1}$
www1.maths.leeds.ac.uk/~pmt6hgd/preprints/… is a great source of knowledge about those things.
Jul
15
comment Constructing a Banach space of cardinality $\beth_{\omega+1}$
Oh, that's easy. Fix $(\mu_i)$ a maximal family of pairwise singular probability measures in $B_0^{**}$. Then you can write $B_0^{**}$ as the $\ell_1$-sum of $L_1(\mu_i)$. In particular, $B_0^{***}$ is the $\ell_\infty$-sum of $L_\infty(\mu_i)$, hence of the form $C(K)$ by Gelfand-Naimark in the complex case or Kalton-Albiac in the real case. Now proceed inductively. General philosophy: the second dual of a C*-algebra is a C*-algebra. Commutativity of the second dual follows from a w*-density argument.
Jul
14
answered Efron-Stein inequality
Jul
14
comment von Neumann Algebras and measures
Your question seems to duplicate this one: mathoverflow.net/questions/137609/…