Real interpolation of functions with applications to accretive operators on Banach spaces

We study real interpolation, but instead of interpolating between Banach spaces, we interpolate between general functions taking values in $[0,\mathrm{\infty }]\mathrm{.}$ We show the equivalence of the mean method and the $K$-method and apply the general theory to interpolation between the norm on a Banach space and the set norm associated with an m-accretive operator on such a space.