Remarks on Lipschitz $p$-summing operators

Abstract:

In this paper, a nonlinear version of the Extrapolation Theorem is proved and, as a corollary, a nonlinear version of Grothendieck’s Theorem is presented. Finally, we prove that if $T:X\to H$ is Lipschitz with $X$ being a pointed metric space and $T(0)=0$ such that $T^\#|_{H^*}$ is $q$-summing $(1\le q<\infty )$, then $T$ is Lipschitz 1-summing.