Timeline for Existence of injective compact operators
Current License: CC BY-SA 4.0
10 events
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May 10, 2020 at 16:37 | comment | added | Bill Johnson | @TamaszKania: And a better one in our recent joint paper. :-) | |
May 10, 2020 at 15:39 | comment | added | Tomasz Kania | @BillJohnson, with the first known example being your space $J\! L$ :-) | |
May 10, 2020 at 13:59 | comment | added | Bill Johnson | Perhaps it is worth pointing out that $X$ has the property if and only if $X^*$ is weak$^*$ separable, which is a somewhat weaker condition than that $X$ embeds isomorphically into $\ell_\infty$. | |
May 10, 2020 at 13:15 | vote | accept | Anupam | ||
May 10, 2020 at 12:19 | history | edited | Tomasz Kania | CC BY-SA 4.0 |
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May 10, 2020 at 12:18 | comment | added | YCor | Thanks, I can see why I was stuck! In any case this provides useful context. | |
May 10, 2020 at 12:17 | comment | added | Tomasz Kania | @YCor, take $T\colon \ell_\infty\to c_0$ given by $T (\xi_k)_{k=1}^\infty = (\xi_k / k)_{k=1}^\infty$. It is compact and injective. | |
May 10, 2020 at 12:16 | history | edited | Tomasz Kania | CC BY-SA 4.0 |
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May 10, 2020 at 12:16 | comment | added | YCor | I was actually trying to check that it never exists if $X$ is non-separable. | |
May 10, 2020 at 12:14 | history | answered | Tomasz Kania | CC BY-SA 4.0 |