Timeline for Weak convergence implies norm convergence for trace class operators?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jan 21, 2016 at 13:21 | comment | added | Nik Weaver | ${\rm Tr}(IT_j) = 1 \not\to 0$. The map $B \mapsto {\rm Tr}(AB)$ is a bounded linear functional on $TC(H)$, for any $A \in B(H)$. | |
| Jan 21, 2016 at 13:13 | comment | added | user1688 | What does that mean? What is the pairingwith the identity? | |
| Jan 21, 2016 at 13:08 | comment | added | Nik Weaver | That's not correct --- your sequence $(T_j)$ converges to zero weak operator, but not weakly. Its pairing with the identity operator doesn't go to zero. | |
| Jan 21, 2016 at 10:17 | history | edited | user1688 | CC BY-SA 3.0 |
added 7 characters in body
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| Jan 21, 2016 at 10:12 | history | answered | user1688 | CC BY-SA 3.0 |