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Abstract

Building upon the interpolation procedure of H. Jarchow and U. Matter for linear operator ideals we define interpolative Lipschitz ideals between metric spaces and Banach spaces. We establish that the resulting class of Lipschitz operators is an injective Banach Lipschitz ideal and show several standard basic properties of that class. We extend the notion of $(p, \theta , q, \nu )$-dominated operator ideal to the Lipschitz setting, we prove the domination theorem in this case and establish several characterizations. Finally, we generalize the interpolative Lipschitz ideal procedure to arbitrary metric spaces and show the Lipschitz ideal properties for this notion.