By a result of Godefroy and Kalton if $X,Y$ are separable Banach spaces and $X$ embeds isometrically into $Y$, then $X$ embeds with a linear isometry into $Y$.
Is this result known to fail for nonseparable spaces? That is, is there a known example of two (necessarily nonseparable) Banach spaces $X,Y$ such that $X$ embeds isometrically into $Y$, but such that there is no linear isometric embedding of $X$ into $Y$?
This question was crossposted to MO and answered there.
This question was answered by Nik Weaver on mathoverflow in the positive: indeed this result is known to be false for nonseparable spaces.