Lipschitz p-integral operators and Lipschitz p-nuclear operators

In this paper, we introduce strongly Lipschitz p-integral operators, strongly Lipschitzp-nuclear operators and Lipschitz p-nuclear operators. It is shown that for a linear operator, the Lipschitz p-nuclear norm is the same as its usual p-nuclear norm under certain conditions. We also prove that the Lipschitz 2-dominated operators and the strongly Lipschitz 2-integral operators are the same with equal norms. Finally, we show that the Lipschitz p-integral norm of a Lipschitz map from a finite metric space into a Banach space is the same as its Lipschitz p-nuclear norm. © 2012 Elsevier Ltd. All rights reserved