BREZIS ANALYSE FONCTIONNELLE PDF

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Isn't normed spaces enough? The particular example I have in mind if theorem III. So why do we need the assumption to be Banach? The only reason for me would be that we use Banach-Steinhaus's theorem BST and thus, we need completeness.

So maybe the completeness is used somewhere I don't see? This is pretty easy to see directly and really misses the point of the theorem. So the authors probably just decided not to bother to include this relatively uninteresting case. It's pretty common in functional analysis to write theorems that only cover Banach spaces, even when normed spaces could also be included. This can be for any of several reasons:. Sign up to join this community.

The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 1 year, 9 months ago. Active 1 year, 9 months ago. Viewed times. Bernard k 8 8 gold badges 46 46 silver badges bronze badges. Peter Peter 1, 2 2 silver badges 13 13 bronze badges. Active Oldest Votes. Nate Eldredge Nate Eldredge So it hold in incomplete vector space as I understood, you said that both side are false in incomplete vector space.

So could you please give me more explanation? The theorem is true for incomplete spaces as well as complete spaces. So it's quite possible the author never used the assumption of completeness.

I don't have a copy of the book to see what's actually written. Eduardo Eduardo 3 3 silver badges 12 12 bronze badges. I have this doubt, but I have never found a reference that said this with all words I'm not pretend know everything, I'm free to be failure Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.

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ALLEGRO 2 EDILINGUA PDF

Functional Analysis, Sobolev Spaces and Partial Differential Equations

By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Isn't normed spaces enough? The particular example I have in mind if theorem III. So why do we need the assumption to be Banach? The only reason for me would be that we use Banach-Steinhaus's theorem BST and thus, we need completeness.

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Analyse fonctionnelle : théorie et applications

It seems that you're in Germany. We have a dedicated site for Germany. Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research.

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