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arXiv · 2506.08458

A study of weak$^*$-weak points of continuity in the unit ball of dual spaces

S. Daptari·V. Montesinos·T. S. S. R. K. Rao
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Abstract

We study classes of Banach spaces where the points of weak$^*$-weak continuity for the identity mapping on the dual unit ball form a weak$^*$-dense and weak$^*$-$G_{\delta}$ set. We also discuss how this property behaves in higher duals of Banach spaces. We prove in particular that if $\mathcal{A}$ is a von Neumann algebra and its predual has the Radon--Nikod\'ym property, then there is no point of weak$^*$-weak continuity on the unit ball of $\mathcal{A}$.

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S. Daptari, V. Montesinos, T. S. S. R. K. Rao. 2025-06-10. A study of weak$^*$-weak points of continuity in the unit ball of dual spaces. https://arxiv.org/abs/2506.08458

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