On the Lipschitz operator ideal Lip0∘A∘Lip0

Abstract

We study a systematic way of producing a Lipschitz operator ideal from a Banach linear operator ideal A. For maximal and minimal operator ideals A, the Lipschitz maximal hull and minimal kernel of the Lipschitz operator ideals Lip0∘A∘Lip0 are investigated, respectively. Using ultraproduct techniques, we obtain the Lipschitz version of a result of Kürsten and Pietsch which characterizes maximal Lipschitz operator ideals. We characterize the linear operators which belong to Lip0∘A∘Lip0; in many cases, they are precisely those which are in A. In particular, we give some cases in which a nonlinear factorization of linear operators implies a linear one, in terms of a given Banach linear operator ideal A.