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yes, I was thinking that too. But there are no reputation points, and no badges there. Just the humble satisfaction of knowing that insights have a permanent, publicly available home.
Ah, but imagine what it would be like to have Bill's answer on the nLab instead of on MO. Then someone who knew what "type" and "cotype" were (or maybe someone who didn't know but knew enough to know how to find out) could come along and add a little explanation which was linked back to the original. Someone else might have something to say about the "infinite dimensional methods" (whatever that means!) and yet another might expand on what Banach did or didn't know. Before you knew it, there'd be a fantastic hyperlinked resource that anyone could easily find.
Nice start, Andrew! Professor Johnson, we at the nLab would love it if you would grace that page with your insights! (No pressure!)
I had been thinking the same thing as Andrew, but didn't start a page because I didn't really understand type and cotype. Which I now see was a silly excuse.
And already Mark Meckes has added the information as to what the types and cotypes of those spaces actually are. Now if only someone could explain what "type" and "cotype" actually mean ...
I would be happy to do so, Andrew, if someone will tell me how to make LaTeX render correctly on Meta.
LaTeX doesn't render on Meta.MO. On the forum that I run for the benefit of nLab users, imaginatively called the nForum, then it does work (you don't have to register to post there if you choose to post in the category 'nLab - latest changes').
But if you're happy for me to take whatever you give me and post it onto the nLab then the simplest might just be to send me it via email (stacey æt math døt ntnu dåt no). The nLab format is sufficiently similar to MathOverflow that if you could paste in into MO it would probably work on the nLab, but also if it is real LaTeX since I have a LaTeX package that can convert real LaTeX to a format suitable for direct inclusion into the nLab, though any reasonable format would be fine.
Forgive my grumpiness, brought on by lack of sleep and a not-entirely-satisfactory lecture, but if us analysts edit that page, will we face lots of cavilling about our notion of isomorphism not being the "correct one"? (There are uses of 1st person plural on the nLab entry for Banach space which makes me think of the old "What do you mean `we', paleface?" joke.)
Ah, I see, Andrew. I emailed you the last version I Previewed on Meta.
Thanks!
Forgive my shouting but, no, you will not. And if you do, complain to me and I'll bang some heads together.
Of course, people will add to entries with categorical viewpoints ("categorical" in the category theory sense, not the functional analytical sense) but I hope that no-one will overwrite or overrule the classical view.
The things to remember about the nLab are:
I added to the page exactly as much as I was sure I could get right without taking the trouble to pull a book off my shelf. (I also added some more elementary comments.)
Regarding Yemon's comment, I hadn't bothered to follow the "isomorphism" link until now. Doing so takes one to a page which contains a definition of the "usual notion of isomorphism" which is squarely at odds with analysts' usage of the term. So something needs to be fixed somewhere. But discussion about this belongs on the nForum and not here.
(Added: I started writing this before the previous two comments appeared.)
More constructively, perhaps Bill might be better placed than me to comment on parts of the entry for "reflexive Banach space"...
Andrew: thanks. Apologies for the peevish tone, it is largely induced by vague guilt at not having read/transcribed enough of Semadeni's tome...
Mark: yes, you're right, this is getting off-topic and discussion should continue on the nForum.
Yemon, I think you mean http://ncatlab.org/nlab/show/reflexive+Banach+space. The link in your question is to this discussion.
Thanks, Andrew; edited. I should really avoid trying to speak Markdown when sleep-deprived...
But discussion about this belongs on the nForum and not here.
Yes, I think that discussion of individual entries belongs on the nForum.
The point I was trying to make with this is that there is a suitable place for answers-without-questions and that there are distinct advantages of putting stuff on the nLab than in an answer to a vague question on MO.
I would also say that functional analysis is extremely welcome on the nLab. I'm a differential topologist, but the spaces that I work with use a lot of functional analysis so I'm keen to learn, and as I learn then I record my notes on the nLab.
I added to the page exactly as much as I was sure I could get right without taking the trouble to pull a book off my shelf.
If everyone did this, we'd have lots of fantastic entries! This is exactly the right attitude when starting with the nLab.
Gil, for a start read my Memoirs with Lior, Gideon, and Bernard. It is only 298 pages. :)
'Course a lot has been done since then.
@Gil Kalai: I should perhaps add that I did not mean to suggest to ask a question verbatim as I sketched them (in addition on a lighter note, I am not an experienced MO-asker, so you can't expect too much if it try to write a question).
Indeed, I do not like MO question written to informally or like an email that much. (Like: Hello Everbody, this and that. Thanks in advance. Signature.) Actually, the split-structure used by the question I linked too, and the one Bill Johnson gave seems really good to me. Those that like motiviation have it, those that don't can ignore it. The mathematical question is there and the motivation and alike can help to fine-tune the answer (or not).
Yet, I also observe that you preceeded the question on Orlicz spaces by a sentence giving motivation 'Thinking about...'. Would you really have omitted this if you had asked the question now on MO, or given it or a link to the previous question?
@Todd Trimble: Thank you for the response. Actually, in part inspired by it, I planned to write something longer and general related to voting. But, meanwhile the thread seems to have taken a different direction. Yet, I am sure there will be other occassions where close/open votes are discussed.
Gil Kalai, basically I agree with all you said in the last comment. I think due the dynamic of the discussion my personal opinion regarding the specific question likely can be perceived as much more critical than it is. In particular, I think both that it was closed and that it then was reopened was reasonable.
A main difference I think really is merely a general procedural one: to me it is reasonable to close in case the situation is unclear/borderline, if/when the situation gets clarified by OP or an expert, then reopen.
Closure is easily reversible, by contrast off-topic, besides-the-point, or generally low quality answers often stay around 'forever'.
In the present case even the a priori risk of such answers was admittedly small, but there are cases where I think this is a real danger (for the overall quality of the site) that should be avoided by temporarily(!) closing.