Timeline for What is the "correct" generalization of operator norms for nonlinear operators?
Current License: CC BY-SA 4.0
16 events
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| Aug 24, 2023 at 16:46 | history | edited | Ben Francis | CC BY-SA 4.0 |
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| Aug 22, 2023 at 22:53 | history | edited | Ben Francis | CC BY-SA 4.0 |
Added context for when this answer might be useful.
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| Aug 22, 2023 at 22:36 | history | edited | Ben Francis | CC BY-SA 4.0 |
Expanded answer to be more precise.
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| Aug 22, 2023 at 22:13 | history | edited | Ben Francis | CC BY-SA 4.0 |
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| Aug 22, 2023 at 22:12 | comment | added | Ben Francis | I am unable to delineate under what circumstances this definition would (or rather would not) be appropriate, but it is the natural generalization of every definition of linear operator norm I have ever seen. | |
| Aug 22, 2023 at 22:08 | comment | added | Ben Francis | There is no reason why the supremum need be finite, even for linear $A$; that's precisely the concept of an unbounded operator: an operator that does not have a finite norm. | |
| Aug 17, 2023 at 22:02 | comment | added | Alex M. | @MaxHorn: And, if that quantity is finite, why is it a norm? | |
| Aug 17, 2023 at 21:38 | comment | added | Max Horn | If $A$ is nonlinear, why should this supremum be finite in general? You hint it might be useful to do this "in some cases". Could you elaborate which cases you have in mind? | |
| Aug 17, 2023 at 21:31 | comment | added | Ben Francis | Corrected to not be a question. | |
| Aug 17, 2023 at 21:31 | history | edited | Ben Francis | CC BY-SA 4.0 |
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| Aug 17, 2023 at 21:23 | comment | added | Max Horn | This does not provide an answer to the question. Once you have sufficient reputation you will be able to comment on any post; instead, provide answers that don't require clarification from the asker. - From Review | |
| S Aug 17, 2023 at 20:42 | review | Low quality posts | |||
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| S Aug 17, 2023 at 20:42 | review | Late answers | |||
| Aug 17, 2023 at 22:02 | |||||
| Aug 17, 2023 at 20:24 | history | edited | Ben Francis | CC BY-SA 4.0 |
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| S Aug 17, 2023 at 20:22 | review | First answers | |||
| Aug 17, 2023 at 20:41 | |||||
| S Aug 17, 2023 at 20:22 | history | answered | Ben Francis | CC BY-SA 4.0 |