Position of $L(X, Y)$ in $Lip_0(X, Y)$
Functional Analysis
2025-06-12 v1
Abstract
We prove that is complemented in (via a norm-one projection) provided that is a dual space. Next, we introduce a vector-valued Lipschitz-free space , a linear contraction and prove that the quotient space is isometrically isomorphic to whenever is injective. We also consider a -valued duality pairing between and and obtain a necessary and sufficient condition for a Lipschitz map to be linear. As an application, we describe as the pre-dual of the quotient space where is the set of all constant maps on .
Keywords
Cite
@article{arxiv.2506.09324,
title = {Position of $L(X, Y)$ in $Lip_0(X, Y)$},
author = {Anil Kumar Karn and Arindam Mandal},
journal= {arXiv preprint arXiv:2506.09324},
year = {2025}
}