Approximation property in terms of Lipschitz maps via tensor product approach

2025/12/06 by Mandal, Arindam
#FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B28 #Secondary 47L20

paper · doi:10.48550/arxiv.2512.06317

Abstract

This article explores the extension of the classical approximation property and its variants to the nonlinear framework of Lipschitz operator theory. Building on Grothendieck's tensor product methodology, we characterize the Lipschitz approximation property of Banach spaces using Lipschitz finite-rank operators and tensor products. Furthermore, inspired by the p-approximation property defined via p-compact sets, we introduce and examine the Lipschitz p-approximation property. We also establish a factorization theorem for dual Lipschitz p-compact operators, mirroring known linear results. This paper looks more closely at how the Lipschitz approximation property and the p-approximation property of a Banach space are related to those of its Lipschitz-free space.

Citations

• Produits tensoriels topologiques et espaces nucléaires

Related

• The approximation property and Lipschitz mappings on Banach spaces
• The approximation property for spaces of Lipschitz functions
• Lipschitz tensor product
• Lipschitz Extensions and Approximations
• The Dual Form of the Approximation Property for a Banach Space and a Subspace