Timeline for Weakly compact operators between Banach spaces
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 28, 2016 at 17:50 | history | edited | M.González | CC BY-SA 3.0 |
correction
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| Dec 17, 2015 at 10:15 | vote | accept | Janko Bracic | ||
| Dec 17, 2015 at 10:15 | comment | added | Janko Bracic | Thank you once more for your answer and useful information. | |
| Dec 17, 2015 at 9:54 | comment | added | M.González | I do not know a general answer; only special cases. Denoting $W(X,Y)$ the weakly compact operators, if $X$ is separable and $L(X,C[0,1])=W(X,C[0,1])$ or $L(X,\ell_\infty)=W(X,\ell_\infty)$, then $X$ is reflexive. If $X$ contains no copies of $\ell_1$ and weakly convergent sequences in $Y$ are norm convergent (like in $\ell_1$) then $B(X,Y)=W(X,Y)$. | |
| Dec 17, 2015 at 8:28 | comment | added | Janko Bracic | Thank you for the answer! My intuition was wrong. Now I see, why I couldn't find an answer to my question in books and papers. However, is there a known general result which says what type of spaces have to be $X$ and $Y$ if every operator in $B(X,Y)$ is weakly compact? | |
| Dec 17, 2015 at 8:12 | history | answered | M.González | CC BY-SA 3.0 |