Timeline for Does the uniform boundedness principle holds for multilinear maps as well?
Current License: CC BY-SA 4.0
11 events
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| Mar 13 at 2:05 | comment | added | Iosif Pinelis | Previous comment continued: (ii) I have now searched for this "standard result" in two not quite elementary FA books and did not find it there. Even the book recommended by TaQ seems to contain only the case of bilinear, rather than general multilinear forms. So, again, can you give at least one specific reference to the "standard result", for general multilinear forms? | |
| Mar 13 at 2:05 | comment | added | Iosif Pinelis | @rediscoveringamerica : (i) I did not use this "standard result" in my proof. Should I have nonetheless acknowledged it? As was noted, my proof is a simple modification of the very short and simple proof for linear functionals. Overall, I think the resulting proof is simpler and shorter than that using the "standard result" (if the proof of that result is included). | |
| Mar 13 at 1:47 | comment | added | Iosif Pinelis | @TaQ : Thank you for the reference. | |
| Mar 12 at 21:21 | comment | added | TaQ | @Isaac Nor is it intended to be such. Something like Rudin's FA, or at least certain parts of it should first be mastered although the specific Theorem 5.1.4 could well be included in a book like that of Rudin's FA, possibly as an exercise with some hints. | |
| Mar 12 at 15:39 | comment | added | Isaac | The book does not seem like some "elementary textbook" on functional analysis to me. | |
| Mar 12 at 14:46 | comment | added | TaQ | @IosifPinelis For example, Jarchow's Locally Convex Spaces has on page 89 Theorem 5.1.4 giving a proof for bilinear maps $E\times F\to G$ when $E$ and $F$ are metrizable tvss with one of them Baire and $G$ a general tvs. | |
| Mar 12 at 14:34 | comment | added | rediscoveringamerica | Well yes, very laudable I am sure, but it is a matter of common courtesy to acknowledge priority (reference: any elementary textbook on functional analysis). | |
| Mar 12 at 13:40 | comment | added | Iosif Pinelis | Can you give a reference to the "standard result"? I vaguely remember seeing it somewhere, but sometimes it is easier for me to prove something than to find it in the literature. | |
| Mar 12 at 12:46 | history | edited | Alex M. | CC BY-SA 4.0 |
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| S Mar 12 at 10:31 | review | First answers | |||
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| S Mar 12 at 10:31 | history | answered | rediscoveringamerica | CC BY-SA 4.0 |