2-Lipschitz Pietsch-$q$-integral and 2-Lipschitz $q$-nuclear operators

Abstract

In this paper, we extend the concept of $q$-nuclear to $2$-Lipschitz mappings. We provide a factorization theorem and establish that a $2$-Lipschitz operator is $q$-nuclear if and only if its transpose is well-defined and $q$-nuclear. Additionally, we introduce the concept of $2$-Lipschitz Pietsch-$q$-integral operators, present a factorization theorem, and demonstrate that this class of operators is generated by the composition method. Conclusively, we demonstrate that every $2$-Lipschitz $q$-nuclear operator is a $2$-Lipschitz Pietsch-$q$-integral operator.