Lipschitz pp-integral operators and Lipschitz pp-nuclear operators

In this paper, we introduce strongly Lipschitz pp-integral operators, strongly Lipschitzpp-nuclear operators and Lipschitz pp-nuclear operators. It is shown that for a linear operator, the Lipschitz pp-nuclear norm is the same as its usual pp-nuclear norm under certain conditions. We also prove that the Lipschitz 22-dominated operators and the strongly Lipschitz 22-integral operators are the same with equal norms. Finally, we show that the Lipschitz pp-integral norm of a Lipschitz map from a finite metric space into a Banach space is the same as its Lipschitz pp-nuclear norm.