Lipschitz interpolative nonlinear ideal procedure

2018/06/15 by Saleh, M. A. S.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1806.06060

Abstract

We treat the general theory of nonlinear ideals and extend as many notions as possible from the linear theory to the nonlinear theory. We define nonlinear ideals with special properties which associate new non-linear ideals to given ones and establish several properties and characterizations of them. Building upon the results of U. Matter we define a Lipschitz interpolative nonlinear ideal procedure between metric spaces and Banach spaces and establish this class of Lipschitz operators is an injective Banach nonlinear ideal and show several standard basic properties for such class. Extending the work of J. A. López Molina and E. A. Sánchez Pérez we define a Lipschitz (p,θ, q, ν)-dominated operators for 1≤ p, q

Related

• Nonlinear Operator Ideals Between Metric Spaces and Banach Spaces (PART I)
• On the Lipschitz operator ideal Lip₀∘ \mathcal A∘ Lip₀
• Building ideals of two-Lipschitz operators between mertic and Banach spaces
• On injective and interpolative procedures for holomorphic Lipschitz ideals
• Lipschitz extensions of linear operators