Mambo

I am stuck with some Commutative diagrams ATM @RollupandsmokeAdjoint

No. It's all $\Bbb R$ intelligence here

That depends on whether or not you think this conversation is actually happening.

Think about a closed rectifiable curve that has every possible winding number

i guess there is no such constructive function. Maybe pull Baire Category or something

@Ted

Sapiens

But I loved the female vocalist's voice.

Listened to a good traditional heavy metal album called "Satan's Hallow" by Satan's Hallow. But they almost copied a Rainbow's song then stopped listening

I guess norm idea won't work. If we let $x_j = (1/j,\frac{1}{2},\ldots,\frac{1}{j},\frac{1}{j},\ldots)$, then we have $f(x_j) = (\frac{1}{j},\frac{1}{2j},\ldots)$

Sure. Thanks for all the help

Apparently there exists some Lipchitz continuous function, a friend of mine said so

Bye @Ted. I am very glad that people are thinking about this

Thank you @Daminark. I was struggling to type it in mobile

Subspace metric

@TedShifrin do you think this is Lipschitz continuous?

What degree do you study @CookieToast?

If there is any linear function, it would mean $c_0$ is complemented in $l_\infty$ which is not true

There is no such linear function

Set of all those sequences that converges to zero

*latter

Trying to think of a continuous function from $$l_\infty$$ to $$c_0$$ that restricts to identity on the lattet

Hi

heloo

Not homework.

On p. 103

pdfs.semanticscholar.org/143b/…

Need French help !!

Hi all

@TedShifrin Look at this sequence construction. Suppose $\sum_n c_n < \infty$. Choose $n_1 < n_2 < \ldots$ such that $\sum_{n > n_k} c_n < 1/2^{-k}$. Now let $b_1 = b_2 = \cdots = b_{n_1} = 1$ and for $ i \geq 1, b_{n_i + 1} = b_{n_i + 2} = \cdots = b_{n_{i+1}} = i+1$. Then $\sum_n b_n c_n$ converges as $\sum_k k/2^{-k}$ converges.

I will follow up on those MSE links. Thanks again

@TedShifrin The very original proof of Riesz brother's theorem : If $\mu$(Borel measure on $[-pi,pi]$) is of analytic type, then it is absolutely continuous wrt Lebesgue measure, uses such construction.

@TedShifrin That's very weird.

@TedShifrin Thank you very much. I am doing that search right on.

Hope :)

@Ted I will search for a more clearer copy

I guess page 17 is the guy

There seem to be so many relevances

yes, I don't read French

I thought Fatou's phd thesis had it, but he referrred to this lecture notes, which I realized just now

I don't understand where exactly it is!

Still stuck at this one :)(

This has a construction of sequence $b_n$ positive tending to infinity such that $\sum b_n c_n$ is finite whenever $sum c_n(>0)$ is finite.

Borel's 1902 lecture notes ia601408.us.archive.org/19/items/leonssurless00boreuoft/…

@Ted

@TedShifrin I guess I mostly worry about my English while posting! I may phrase it so bad that people don't usually answer :(

Very nice :D

Any help will be appreciated.

I am looking for a result in a French paper