Timeline for Extending compact operators into $c_0$

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Aug 12, 2013 at 13:36	comment	added	Ben W		Awesome, thank you for the reference! Regarding your comment, it's a good idea and one that I had considered. However the problem is commutation. Suppose $X=Y_0\oplus Z_0$ where $S:=T\|_{Y_0}\oplus 0$ is compact. We need to show that $TS=ST$. Then given $y+z\in X$ we have $TS(y+z)=T^2y$, but $ST(y+z)=T^2y$ only if $Tz\in Y_0$. Still, it's a good idea and one I intend to keep in mind as I research.
Aug 12, 2013 at 1:16	history	edited	Tomasz Kania	CC BY-SA 3.0	+more
Aug 12, 2013 at 1:04	history	answered	Tomasz Kania	CC BY-SA 3.0