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I've started a page an elementary treatment of Hilbert spaces. The intention is to see how much of (simple) Hilbert space theory can be done without using the phrases "As a Hilbert space is a normed vector space ..." or "As a Hilbert space is a metric space ...".
I haven't gotten very far yet, as can be seen! Also, it's not intended to be Deep Mathematics (there's a mild centipedal justification on the page) but just playing with some ideas and trying to see what a Hilbert space really is.
I slightly Lab-elved the page, editing the toc and insering some links
Thanks!
I should have said: I hope that this is okay for the n-lab.
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I hope that this is okay for the n-lab.
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<p>Most certainly. Why are you worried?</p>
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It didn't have an 'n' in it!
I wasn't particularly worried, otherwise I would have asked before I started writing, but I suffer from the British disease of always worrying that I'm in the wrong place at the wrong time.
Well, I think thi stuff is very good. It doesn't need to have an n in it to be part of the nLab.
Yeah, you just have to accept that we'll start remarking on what strength of logic your elementary treatment requires and which categories it can be internalised in, stuff like that.
@Toby, go ahead!
Seriously, so long as it's clear which bits are meant as the "elementary" bits and which are commentary, then I would welcome such. As you can see, I'm putting in remarks linking the elementary treatment to the standard treatment. In case it's not clear, the idea of such an elementary treatment is that it be a gateway to the more developed theory but one that is, perhaps, simpler to reach. Without the commentary there wouldn't be any indication of where someone could go once they'd gotten through the gateway. So I see remarks like that as sort of "If you liked this bit, you'll also like ...".
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