The approximation property and Lipschitz mappings on Banach spaces
Pilar Rueda, Enrique A. Sanchez-Perez
TL;DR
This paper reviews the approximation property in Banach spaces, focusing on recent links to operator ideals and Lipschitz mappings, and introduces new results on approximating Lipschitz functions.
Contribution
It provides a comprehensive overview of the approximation property and introduces new findings on Lipschitz mappings and their relation to operator ideals.
Findings
New results on approximation of Lipschitz mappings
Connections between Lipschitz ideals and linear operator ideals
Enhanced understanding of the approximation property in Banach spaces
Abstract
We present an overview to the approximation property, paying especial attention to the recent results relating the approximation property to ideals of linear operators and Lipschitz ideals. We complete the paper with some new results on approximation of Lipschitz mappings and their relation to linear operator ideals.
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Taxonomy
TopicsAdvanced Banach Space Theory · Approximation Theory and Sequence Spaces · Fixed Point Theorems Analysis