Relationship between Sublinear Operators and their Subdifferentials for Certain Classes of Lipschitz Summability
Authors: Ferradi Athmane , Mezrag Lahcene 
Published: January 2025

Let SB(X, Y ) be the set of all bounded sublinear operators from a Banach space X into a complete Banach lattice Y ;which is a pointed convex cone not salient in Lip0(X, Y ). In this paper, we are interested in studying the relationship between T and itssubdifferential ∇T (the set of all bounded linear operators u : X -→ Y such that u(x) ≤ T (x) for all x in X); concerning certainnotions of Lipschitz summability. We also answer negatively a question posed previously concerning this type of relation in the linearcase. For this, we introduce and study a new concept of summability in the category of Lipschitz operators, which we call ”superLipschitz p-summing operators”. We prove some characterizations in terms of a domination theorem and some properties of this notion. 
MSC: Primary 46B25, 46T99; Secondary 47H99, 47L20
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Communicated Editor: Berbiche MohamedManuscript received Jan 17, 2024; revised Mar 27, 2024; accepted Apr 10, 2024; published May 13, 2024.