/sci/ - Science & Math » Thread #11288766

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Anonymous Thu 09 Jan 12:43:14 2020 No.11288766 View Reply Original Report

Quoted By: >>11288797 >>11288834 >>11289514

Any functional analysis fags here?

My teacher gave us homework and i suspect one of the questions is impossible. Am i just going crazy here?

Anonymous

Anonymous Thu 09 Jan 2020 12:47:02 No.11288770 Report

Quoted By: >>11289514

This looks a lot like Lipschitz stuff, I'll see if I can find to think about it

Anonymous

Anonymous Thu 09 Jan 2020 12:51:50 No.11288778 Report

Quoted By: >>11289514

Doesn't this contradict what the exercise says?

http://mathonline.wikidot.com/criterion-for-b-x-y-to-be-a-banach-space

Anonymous

Anonymous Thu 09 Jan 2020 13:06:22 No.11288797 Report

Quoted By: >>11288814 >>11288935 >>11289514

>>11288766
Hahahaha
Your teacher is a dick

Anonymous

Anonymous Thu 09 Jan 2020 13:23:20 No.11288814 Report

Quoted By: >>11289125 >>11289514

>>11288797
So it CANT be solved?

Anonymous

Anonymous Thu 09 Jan 2020 13:42:53 No.11288834 Report

Quoted By: >>11288869 >>11288879 >>11288914 >>11288935 >>11289514

>>11288766
Consider
E = Set of finite sequences of real numbers with l1-norm.
F = Set of real numbers with absolute value as norm.
T_n(x_1, x_2, ... ) = x_n
Then
T(x) = 0
but (T_n) doesn't converge to 0 since for every n you can find a sequence x with T_n(x) = 1.

Anonymous

Anonymous Thu 09 Jan 2020 14:01:11 No.11288869 Report

Quoted By: >>11289514

>>11288834
Oh wow! Thanks! I will have to read some proofs again because i definitely missed something. Great example

Anonymous

Anonymous Thu 09 Jan 2020 14:05:47 No.11288879 Report

Quoted By: >>11288900 >>11289514

>>11288834
>E = Set of finite sequences of real numbers with l1-norm.
>F = Set of real numbers with absolute value as norm.
>T_n(x_1, x_2, ... ) = x_n
>Then
>T(x) = 0

how is T_n defined for finite sequences of length less than n?

Anonymous

Anonymous Thu 09 Jan 2020 14:15:02 No.11288900 Report

Quoted By: >>11288912

>>11288879
You can just remove the word finite. It will still work with $E=l^1(\mathbb{R})$ .

Anonymous

Anonymous Thu 09 Jan 2020 14:24:10 No.11288912 Report

Quoted By:

>>11288900

bear with me, i've never taken functional analysis.

your T isn't defined on all of E, right? the sequence T_n(x) does not converge unless x converges.

Anonymous

Anonymous Thu 09 Jan 2020 14:25:40 No.11288914 Report

Quoted By: >>11289514

>>11288834
>considering a linear functional as a linear operator
>borrowing the oldest example in the book about weak convergence of functionals not being equal to convergence of functionals
I rate your counterexample constructing skills a solid 9/10.

Anonymous

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Anonymous Thu 09 Jan 2020 14:41:21 No.11288935 Report

Quoted By: >>11289155 >>11289514

>>11288797
>>11288834
Another demonstration that laughing is indeed low IQ behavior.

Anonymous

Anonymous Thu 09 Jan 2020 16:58:39 No.11289125 Report

Quoted By: >>11289514

>>11288814
Dunno im studying medicine
Wanna know something about Organs and shit

Anonymous

Anonymous Thu 09 Jan 2020 17:17:02 No.11289155 Report

Quoted By: >>11289189 >>11289514

>>11288935
I rarely laugh but still have low IQ. Explain this anon

Anonymous

Anonymous Thu 09 Jan 2020 17:41:51 No.11289189 Report

Quoted By: >>11289514

>>11289155
He’s just upset that he has low verbal iq, the character of one’s laughter and sense of humor says more about your intelligence than whether you express laughter.

Anonymous

Anonymous Thu 09 Jan 2020 19:16:32 No.11289346 Report

Quoted By: >>11289514

God I fucking hated functional analysis

Anonymous

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Anonymous Thu 09 Jan 2020 20:39:08 No.11289514 Report

Quoted By: >>11289614

>>11288766
>>11288770
>>11288778
>>11288797
>>11288814
>>11288869
>>11288879
>>11288914
>>11288935
>>11289125
>>11289155
>>11289189
>>11289346
very very low iq, never post again
>>11288834
room temp iq, fine, but consider waiting a few years before you post again

Anonymous

Anonymous Thu 09 Jan 2020 21:22:13 No.11289614 Report

Quoted By:

>>11289514
imagine spending the time replying to all these posts

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