Timeline for Hölder continuity of functional calculus
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Oct 21, 2020 at 1:13 | vote | accept | Paul Pfeiffer | ||
| Oct 20, 2020 at 22:44 | history | became hot network question | |||
| Oct 20, 2020 at 16:43 | answer | added | Mikael de la Salle | timeline score: 7 | |
| Oct 20, 2020 at 15:51 | comment | added | Paul Pfeiffer | That approach does not work. For my application, the assumption, that $A$ is trace class is satisfied, but I am also interested in the case, where $A$ is not trace class. | |
| Oct 20, 2020 at 15:43 | comment | added | Yemon Choi | And what about $A$? Your reference to singular values in the comment above suggests you want both A+B and B to be trace-class. | |
| Oct 20, 2020 at 15:19 | history | edited | Paul Pfeiffer | CC BY-SA 4.0 |
mentioned Schatten semi norm
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| Oct 20, 2020 at 15:18 | comment | added | Paul Pfeiffer | If $B$ is not trace class, or more general not in the $\beta$- Schatten von Neumann class, the right hand side is infinite and hence the statement is tautolgical. So you may assume $B$ to be trace class. | |
| Oct 20, 2020 at 15:16 | comment | added | Paul Pfeiffer | My first approach does not work. Even for commutating operators, we would need to rearrenge the singular values of $B$ to make this work. This is probably not a good approach. | |
| Oct 20, 2020 at 15:16 | comment | added | Yemon Choi | If you are working in infinite dimensions, are you including the assumption that B is trace-class? Your question talks of self-adjoint operators on Hilbert spaces but these might not have SVD etc | |
| Oct 20, 2020 at 15:07 | comment | added | Paul Pfeiffer | For the first statement, it is sufficient to show, that for the ordered singular values, we have the inequality $\lvert s_i(A+B)-s_i(A) \rvert \le s_i(B)$ using the assumption $0 \le A,A+B \le1$. | |
| S Oct 20, 2020 at 14:50 | history | suggested | gmvh |
Added top-level tag and "inequalities" tag (since the question is about establishing a certain inequality)
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| Oct 20, 2020 at 14:49 | review | Suggested edits | |||
| S Oct 20, 2020 at 14:50 | |||||
| Oct 20, 2020 at 14:45 | history | edited | Paul Pfeiffer | CC BY-SA 4.0 |
even stronger second hypothesis
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| Oct 20, 2020 at 14:38 | history | asked | Paul Pfeiffer | CC BY-SA 4.0 |