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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
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10h
comment Maximal Ideals and Maximal Subspaces in normed algebras
Thank you Jonas, corrected!
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revised Maximal Ideals and Maximal Subspaces in normed algebras
corrected
16h
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.
21h
revised Maximal Ideals and Maximal Subspaces in normed algebras
serious correcrions
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awarded  Mortarboard
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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.
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revised Maximal Ideals and Maximal Subspaces in normed algebras
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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.
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revised Maximal Ideals and Maximal Subspaces in normed algebras
-,
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comment Maximal Ideals and Maximal Subspaces in normed algebras
I have improved my answer.
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revised Maximal Ideals and Maximal Subspaces in normed algebras
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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/…