Mathematics - 2023-06-14 (page 3 of 3)

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shintuku

22:00

ok yeah it makes full sense now, thanks a lot lads

D.C. the III

@XanderHenderson Oh.....no, no , no, no Xander. I will not allow you to besmirch the name of Saint Seiya or as it was known in Latin America: Los Caballeros del Zodiaco...............those are grounds to report you to the mods........

s.harp

whats the bidual of C[0,1]? Is there a nice description?

leslie townes

22:16

"the bidual of C[0,1]" is the nicest description i know of. it's the usual tradeoff of, you can get a more 'concrete-sounding' description at the cost of introducing really shitty spaces. ("oh, it's just the space of vector-valued charges on the stone space of the ...")

Q: Double dual of the space $C[0,1]$

The second dual or double dual of the space of all continuous functions on $[0,1]$, $C[0,1]$ is von Neumann algebra. Can anyone help me identifying this space?

Jakobian

it reminds me how you need quadruple duals or something to prove a result by James

sometimes you need to stack them a lot

s.harp

oh right, its the enveloping vN algebra... forgot that they are all nightmares

Jakobian

I haven't been reading any functional analysis in some time now

leslie townes

when you're paid by the asterisk

s.harp

who wrote that

and why

leslie townes

22:33

i don't actually know, it's from a screenshot i took a long time ago. maybe from sakai, but i lost that book in a move

Jakobian

I think you posted this image before and even explained who wrote it

leslie townes

it's part of a proof that if F_1 is a subspace of a banach space F and there is a norm-one projection of F onto F_1, then for any banach space E, E tensor F_1 embeds in E tensor F (projective tensor product)

something like that is probably in sakai even if that isn't from sakai

s.harp

The text looks like sakai

I have the book here, I stole it from some guy who was moving

leslie townes

it's weird because i somehow illegally downloaded an electronic version of sakai that did not have this material, but my vague memory was that it was in sakai, and i am sure that i owned this in print, and i owned sakai in print

but shrug

Jakobian

Jun 2, 2021 at 23:57, by leslie townes

reminds me of one of my favorite looking pages of sakai.

leslie townes

22:37

let's say it's sakai

two years pass and here i am, still just talkin' bout asterisks in sakai

Jakobian

yep chat.stackexchange.com/transcript/36?m=58212984#58212984

s.harp

Man this copy stinks of old beer ( I actually bought it from the net and didn’t steal it) no wonder I never read more than the forst chapter

Jakobian

once every year

Sep 28, 2022 at 17:41, by leslie townes

i dunno, ask sakai

shintuku

so sad steve jobs died of sakai

mick

Q: Prime gap conjecture $ \pi_{2a}(n+(6a+4)^3)+(6a+4)^3 > \pi_{4a}(n)$ counterexamples?

Consider prime constellations $p,p+2s$ where both $p,p+2s$ are prime. For instance for $s=1$ we get the twin primes. We define the counting function $\pi_{2s}(n)$ to count the number of such pairs $p,p+2s$ below or equal to $n$. Does this conjecture hold ? $$ \pi_{2a}(n+(6a+4)^3)+(6a+4)^3 > \pi_{...

number-theory inequality prime-numbers prime-gaps prime-twins

probably counterexamples are known or computable ...

冥王 Hades

22:55

God knew I’d be too powerful if I also had social skills

Sine of the Time

Is it better studying math at night or early morning?

leslie townes

23:10

mm, i don't think there's anything specific to math about that. if you are a 'morning person' or 'evening person' with other stuff, probably same for math.

shintuku

23:25

as i get deeper into the week i gain full consciousness later and later in the day

morning math only possible first three days

Jakobian

@leslietownes does such people exist?

I find doing math, hour or two after waking up, then you get distracted and start doing math whenever again, be it evening or not