Normal functionals on Lipschitz spaces are weak$^\ast$ continuous

Ramón J. Aliaga; Eva Pernecká

doi:10.1017/S147474802100013X

Normal functionals on Lipschitz spaces are weak$^\ast$ continuous

Functional Analysis 2023-02-28 v2

Authors: Ramón J. Aliaga , Eva Pernecká

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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.

Keywords

lipschitz spaces function theory

Cite

@article{arxiv.2004.14310,
  title  = {Normal functionals on Lipschitz spaces are weak$^\ast$ continuous},
  author = {Ramón J. Aliaga and Eva Pernecká},
  journal= {arXiv preprint arXiv:2004.14310},
  year   = {2023}
}

Comments

v2: Revised version

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