Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 12, Number 1 (2018), 240-257.
Weighted Banach spaces of Lipschitz functions
Given a pointed metric space and a weight on (the complement of the diagonal set in ), let and denote the Banach spaces of all scalar-valued Lipschitz functions on vanishing at the basepoint such that is bounded and vanishes at infinity on , respectively, where is the de Leeuw’s map of on , under the weighted Lipschitz norm. The space has an isometric predual and it is proved that and , where denotes the bounded weak∗ topology and the topology of uniform convergence on compact sets. The linearization of the elements of is also tackled. Assuming that is compact, we address the question as to when is canonically isometrically isomorphic to , and we show that this is the case whenever is an M-ideal in and the so-called associated weights and coincide.
Banach J. Math. Anal., Volume 12, Number 1 (2018), 240-257.
Received: 12 April 2017
Accepted: 7 July 2017
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46E15: Banach spaces of continuous, differentiable or analytic functions
Secondary: 46A20: Duality theory
Jiménez-Vargas, A. Weighted Banach spaces of Lipschitz functions. Banach J. Math. Anal. 12 (2018), no. 1, 240--257. doi:10.1215/17358787-2017-0030. https://projecteuclid.org/euclid.bjma/1513674119