Timeline for When does $\left\Vert f(\mathbf{N}) - f(\mathbf{M})\right\Vert_{\mathrm{op}} \leq k\left\Vert \mathbf{N} - \mathbf{M}\right\Vert_{\mathrm{op}}$ hold?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 7, 2020 at 20:18 | comment | added | Yemon Choi | @Henry No worries! Actually, I think you should probably "accept" Mikael's answer instead of mine since he actually provided more precise references. In particular, the Besov space approach that Aleksandrov and Peller looks like it might provide what you need. | |
| Oct 7, 2020 at 9:41 | vote | accept | Henry | ||
| Oct 8, 2020 at 15:06 | |||||
| Oct 7, 2020 at 9:36 | comment | added | Henry | Hi Yemon, thank you for your answer. I appreciate your patience with my lack of understanding in this field. It's very useful for me to know that the papers of Aleksandrov and Peller are about the operator norm. I understand that Lipschitz might not imply operator Lipschitz and even in the cases a function is both the constants may not be the same. I don't think I communicated it well but my question is what conditions can I find so that this is the case. Theorem 3.14.1 in the survey gives me a necessary condition for the constants to be equal, but I'm really after some sufficient conditions | |
| Oct 5, 2020 at 14:43 | comment | added | Mikael de la Salle | Yes, we more or less wrote the same answer... | |
| Oct 5, 2020 at 14:41 | comment | added | Yemon Choi | I think Mikael de la Salle's answer has said what I was trying to get at, but with more precise details | |
| Oct 5, 2020 at 14:38 | history | answered | Yemon Choi | CC BY-SA 4.0 |