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May
25
comment Characterization of $l_p$ up to a linear isometry
Bill, that idea with facets, did it get any formalization in the question about $\ell_\infty$?
May
25
comment Characterization of $l_p$ up to a linear isometry
Ah, OK, thank you. Do your words mean that infinite dimensional $\ell_\infty$ were not characterised?
May
25
comment Characterization of $l_p$ up to a linear isometry
Bill, before I find this reading, what is "1 symmetric basis"?
May
25
comment Characterization of $l_p$ up to a linear isometry
And what about other $\ell_p$?
May
25
comment Characterization of $l_p$ up to a linear isometry
Bill, first, excuse me, what is $\ell_\infty^*$? And that is interesting, of course, but it sounds not quite geometrically, more in terms of category theory.
May
25
comment Characterization of $l_p$ up to a linear isometry
@Mark Meckes: I think, this depends on the definition of facet. And I have no idea about $p\notin\{1,2,\infty\}$, I thought this must be digged up.
May
25
revised Characterization of $l_p$ up to a linear isometry
specification
May
25
comment Characterization of $l_p$ up to a linear isometry
For example, as far as I understand, the following statement is true: a Banach space $X$ is isometrically isomorphic to $\ell_1^n$, $n\in{\mathbb N}$, if and only if $\dim X=n$, and the unit ball of $X$ has exactly $2n$ extreme points. Is something similar true, say, for $\ell_\infty^n$?
May
25
comment Characterization of $l_p$ up to a linear isometry
Bill, of course I mean another thing. The question is which geometric properties of (the unit ball in) a Banach space $X$ allow us to conclude that $X$ is isometrically isomorphic to $\ell_p^n$. And I don't ask about Hilbert spaces.
May
25
comment Characterization of $l_p$ up to a linear isometry
Bill, this classification where is it described? And what is not clear in my question?
May
25
asked Characterization of $l_p$ up to a linear isometry
May
23
comment What is a continuous path?
There was a little book by A.S.Parhomenko "What line is" (printed in 1954 in USSR). He gives the following definition of line with a reference to P.S.Urysohn: 1) a connected compact topological spaces is called continuum, 2) a continuum $C$ in $\mathbb R^2$ in called line, if for each point $x\in C$ and for each $\varepsilon>0$ there is a neighborhood $U$ of $x$ of diameter $<\varepsilon$ such that the boundary $\partial U$ of $U$ contains only singletons as continuums.
May
22
comment Can a continuous function on a compact group $G$ be interpreted as the sum in $C(G)$ of its Fourier series?
Hm... I had a hope that there is a paper that I can refer to... :) OK, Paul, thank you.
May
21
comment Can a continuous function on a compact group $G$ be interpreted as the sum in $C(G)$ of its Fourier series?
Marc Palm refers to a Harish-Chandra paper here mathoverflow.net/questions/162856/…. Paul, do you mean these results or something else?
May
20
awarded  Nice Question
May
20
revised Can a continuous function on a compact group $G$ be interpreted as the sum in $C(G)$ of its Fourier series?
added 305 characters in body
May
19
comment Fourier series of functions on compact groups
Marc, could you, please, advise reading about the case of $C^\infty$?
May
18
comment Can a continuous function on a compact group $G$ be interpreted as the sum in $C(G)$ of its Fourier series?
Ah, OK, thank you, I did it.
May
18
comment Can a continuous function on a compact group $G$ be interpreted as the sum in $C(G)$ of its Fourier series?
Yes, I think that there must (probably) be a tricky summation method like the Fejér one.
May
18
comment Can a continuous function on a compact group $G$ be interpreted as the sum in $C(G)$ of its Fourier series?
I gave the link to MSE. Or do you mean this link: mathoverflow.net/questions/162856/…?