Timeline for Convergence of nuclear operators
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 11, 2018 at 7:12 | vote | accept | Alexander Kukush | ||
| Jun 11, 2018 at 7:07 | comment | added | Alexander Kukush | @fedija Now I understand your solution thoroughly. Brilliant! You helped me a lot. As a result I have a criterion for weak convergence of Gaussian measures in H: Measures $N(m_n, S_n)$ converge weakly to $N(m, S)$ if, and only if, $m_n$ converges strongly to $m$ and $S_n$ converges to $S$ in nuclear norm. | |
| Jun 10, 2018 at 20:34 | comment | added | fedja | @AlexanderKukush $\delta(P_nA_kP_n+P_nAP_n)+\delta^{-1}(P^nA_kP^n+P^nAP^n)$ dominates the "off-diagonal" part of $A_k-A$; $\delta n^{-1}P_n$ is just to dominate $-P_n(A_k-A)P_n$. Is that much clear? | |
| Jun 10, 2018 at 20:23 | comment | added | Alexander Kukush | Alas, in the proposed answer I do not see why this long operator is positive for large k and fixed n, $\delta.$ And I cannot understand the origin of the term $\delta n^{-1} P_n$. | |
| Jun 10, 2018 at 19:12 | history | answered | fedja | CC BY-SA 4.0 |