Equivalences between certain properties of weighted Lipschitz operators
Abstract
We show that for a weighted Lipschitz operator $ω\widehat{f}$, certain linear properties are equivalent. Specifically, we prove that compactness, strict singularity, and strict cosingularity are all equivalent to the property of not fixing any complemented copy of $\ell^1$. Then we generalize this result to operators between Lipschitz-free spaces that preserve finitely supported elements, a larger class of operators.
Fields of Study & Subjects
Advanced Banach Space Theory
Advanced Harmonic Analysis Research
Approximation Theory and Sequence Spaces
Publication details
- Journal / source
- Journal of Mathematical Analysis and Applications
- Volume
- 568
- Issue
- 1
- Pages
- 131164–131164
- Publication date
- 21 October 2026
- Language
- EN