Assume that $X$ and $Y$ are two Banach spaces and $T:X\to Y$ is a bounded surjective linear operator.

A consequence of the Michael selection theorem is that:"There is a continuous function $g:Y\to X$ such that $T\circ g=Id_{Y}$".

Can we always find a linear map $g$ as above?

continuousselection andlinearselection (playing with Hamel bases) but of course not always acontinuous linearone. – Jochen Wengenroth Mar 24 at 7:33