On the summability of nonlinear mappings

Abstract

This work focuses on two examples of nonlinear operator ideals: the ideal of Lipschitz p summing operators and the ideal of p-summing weighted holomorphic mappings. The First one was introduced by Farmer and Johnson in 2009 , and the second one by M. G. Cabrera Padilla, A. Jiménez-Vargas and A. Keten Çopurin 2024 . In each category, we establish the corresponding Pietsch Domination and Factorization theorems. Finally, by equipping a suitable tensor product with an appropriate Chevet–Saphar–type norm, we identify the dual of the space of p-summing weighted holomorphic mappings.