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

TL;DR

This paper develops a new approach to real interpolation by interpolating between functions rather than spaces, establishing equivalences between methods, and applying this theory to accretive operators on Banach spaces.

Contribution

It introduces a novel interpolation framework for functions valued in [0,∞) and applies it to analyze accretive operators in Banach spaces.

Findings

Equivalence of mean and K-methods in the new interpolation framework

Application of the theory to m-accretive operators

Enhanced understanding of interpolation between norms and set norms

Abstract

We study real interpolation, but instead of interpolating between Banach spaces, we interpolate between general functions taking values in $[0,\infty].$ 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.