Timeline for On compact operators with domain $c_{0}$

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Oct 3, 2015 at 21:34	comment	added	Dongyang Chen		I forget the basic fact mainly because I have never taught functional analysis in my university. In fact, in my question, we can let $S=T^{}J_{X}$, where $J_{X}:X\rightarrow X^{*}$ is the canonical embedding. Anyway, thanks, Bill.
Oct 3, 2015 at 18:47	comment	added	Bill Johnson		Yes. If $T:Y\to X^$ is even just weakly compact, then $T^{}$ maps $Y^{}$ into $X^$ and extends $T$. In a first course in functional analysis one should learn that an bounded linear operator $S:V\to U$ is weakly compact if and only if $S^{}V^{} \subset U^{**}$. So this question is arguably more appropriate for another site. (I say ``arguably" because such a basic fact is probably hard to find in text books on real analysis.)
Oct 3, 2015 at 16:32	history	asked	Dongyang Chen	CC BY-SA 3.0