@Huy I think I already asked you this, did you skip the first chapter?

Is chapter 1 meant to be referred to periodically as we pass through the text?

Nvm I investigated the previous room:

I have started chapter 2

@GaloisintheField: I think it says it at the beginning of the book or chapter that it is just a collection of applications of functional analysis that can be skipped. I looked through the more interesting ones for me (ODEs, PDEs), some others I skipped. Just personal preference really, it's not important for what comes next.

I have to teach soon, maybe I have time in the afternoon (I'm in German time zone)

Okay, I just didn't get that norm

I can wait until later

what about it?

So $B\subset\Bbb R^d$ and the norm takes the minimal positive $\lambda$ that puts $\frac1\lambda v$ into $B$?

yea

Oh I see, centrally symmetric

imagine for example the unit ball and then some vector in $\mathbb{R}^2$

For some reason I was thinking it was symmetry anywhere haha

you can easily see that there exists such a $\lambda$ then

to scale the vector back into the unit ball

Yeah that works

That's a pretty damn cool norm too

yea

I wonder where it has its applications

:D

pshhh who needs applications :P

I'm sure you already know this from algebra but just take the most trivial examples when encountering new definitions and then it's much easier to understand

maybe it's more important in analysis because algebra is more abstract but idk

Yeah I did, but I put the ball off the center and it seemed false haha

^^

ok I'm off to teach

Have fun!

if there's anything just ping me and write the question, I'll have a look at it asap

Sounds good :)

@GaloisintheField: you're not at Thm 3.3 already by any chance? I'm looking at the proof and I think it's really cool that something this "big" is so "easy" to prove

@Huy Are you saying the spectral theorem of compact abelian groups?

If so that's probably atleast 15 days away haha