Normal functionals on Lipschitz spaces are weak$^\ast$ continuous
Abstract
Let $\operatorname{Lip}_0(M)$ be the space of Lipschitz functions on a complete metric space $M$ that vanish at a base point. We show that every normal functional in $\operatorname{Lip}_0(M)^\ast$ is weak$^*$ continuous, answering a question by N. Weaver.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2020
- DOI:
- 10.48550/arXiv.2004.14310
- arXiv:
- arXiv:2004.14310
- Bibcode:
- 2020arXiv200414310A
- Keywords:
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- Mathematics - Functional Analysis;
- 46B20;
- 46E15
- E-Print:
- v2: Revised version