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visits member for 1 year, 11 months
seen Dec 18 at 21:31

I guess I'm a graduate student now. That's a little weird.

This will remain the account that I use to anonymously ask stupid questions.


Dec
15
awarded  Caucus
Dec
10
revised Prove that if $f$ is integrable on $[0,1]$, then $\lim_{n→∞}\int_{0}^{1} x^{n}f(x)dx = 0$.
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Dec
10
comment Prove that if $f$ is integrable on $[0,1]$, then $\lim_{n→∞}\int_{0}^{1} x^{n}f(x)dx = 0$.
@NateEldredge Haha, that's true too. This was just what immediately came to mind, so I wrote it down for posterity. :)
Dec
10
revised Prove that if $f$ is integrable on $[0,1]$, then $\lim_{n→∞}\int_{0}^{1} x^{n}f(x)dx = 0$.
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Dec
10
answered Prove that if $f$ is integrable on $[0,1]$, then $\lim_{n→∞}\int_{0}^{1} x^{n}f(x)dx = 0$.
Dec
9
revised Let $X$ and $Y$ be Banach, and $T : X \to Y$ a bounded linear map. When is $T$ closed?
added 46 characters in body
Dec
9
comment Let $X$ and $Y$ be Banach, and $T : X \to Y$ a bounded linear map. When is $T$ closed?
I am trying to argue that the Schwartz class S is not normable by displaying it as a dense subspace of $L^1$, and then trying to argue that (given normability) the inclusion can be upgraded to surjectivity (which is nonsense), by showing that the range is closed. Since I don't know what the norm looks like, I wanted to make use of some less analytical property of $S$ in order to show that the range is closed.
Dec
9
comment Let $X$ and $Y$ be Banach, and $T : X \to Y$ a bounded linear map. When is $T$ closed?
Thanks, good point. I think in my mind (and at least in the problem I was working on), $T$ was implicitely injective.
Dec
9
revised Let $X$ and $Y$ be Banach, and $T : X \to Y$ a bounded linear map. When is $T$ closed?
added 64 characters in body
Dec
9
comment Let $X$ and $Y$ be Banach, and $T : X \to Y$ a bounded linear map. When is $T$ closed?
Sorry, yes, I mean that $im T$ is closed, not that the graph of $T$ is closed.
Dec
9
asked Let $X$ and $Y$ be Banach, and $T : X \to Y$ a bounded linear map. When is $T$ closed?
Dec
9
revised Why should the open mapping theorem be expected?
added 30 characters in body
Dec
9
asked Why should the open mapping theorem be expected?
Dec
8
asked Let $B$ be the Banach space of complex measures, with norm $|\mu|(X)$. What is the Banach space interpretation of notions such as mutual singularity?
Dec
6
accepted Is it sufficient to check weak convergence on a (weak* or strongly) dense subset of the dual?
Dec
6
asked Is it sufficient to check weak convergence on a (weak* or strongly) dense subset of the dual?
Dec
1
comment Problem in proving that $\mathbb{A}^2$ is not homeomorphic to $\mathbb{P}^2$
Any two curves in $P^2$ have a nonempty intersection.
Nov
29
comment Number of elements of a prime ideal's coset
Yes, that is what I was doing.
Nov
29
comment Number of elements of a prime ideal's coset
Yes, that is what I meant, thanks.
Nov
28
comment Number of elements of a prime ideal's coset
There are only two elements in $Z / 2Z$, and the only nonzero one is $1 + Z$, which has an obvious inverse. The cosets of an ideal are the elements of the quotient ring, and the quotient ring given by modding out by the kernel is isomorphic to the image of the ring homomorphism. An isomorphism is in particular a bijection.