Suppose $X$ is a normed linear space and $Y\subset X$ a linear subspace.
I remember that any linear map $L\colon Y\to L^\infty(\Omega)$ can be extended to a linear map $\tilde{L}\colon X\to L^\infty(\Omega)$ that has the same operator norm. (Under some assumptions, I guess $\sigma$-finiteness, on the measure that on $\Omega$)
Does anyone have a reference for that?
