LIPSCHITZ p-INTEGRAL OPERATORS AND LIPSCHITZ p-NUCLEAR OPERATORS

In this note we introduce strongly Lipschitz p-integral operators, strongly Lipschitz p-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.