1,024 reputation
1515
bio website mathnet.ru/php/…
location
age
visits member for 2 years, 10 months
seen 24 mins ago

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/…?
May
18
asked Can a continuous function on a compact group $G$ be interpreted as the sum in $C(G)$ of its Fourier series?
May
18
comment Fourier series of functions on compact groups
Is it possible that for continuous $f$ (and for arbitrary compact group $G$) the pointwise convergence can always be understood in some specific sense, like for example the Fejér theorem en.wikipedia.org/wiki/Fej%C3%A9r%27s_theorem suggests?
Mar
29
asked Uniform structure on the Banach bundle generated by a Banach module
Jan
18
comment Is every distribution a linear combination of Dirac deltas?
A reference: W.Rudin, 6.26.
Jan
17
revised What are your favorite concrete examples of limits or colimits that you would compute during lunch?
deleted 55 characters in body
Jan
17
revised What are your favorite concrete examples of limits or colimits that you would compute during lunch?
edited body