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arXiv · 2506.09786

Lipschitz free $p$-spaces for $0<p<1$ in the light of the Schur $p$-property and the compact reduction

Fernando Albiac·José L. Ansorena·Jan Bíma·Marek Cúth
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Abstract

The geometric analysis of non-locally convex quasi-Banach spaces presents rich and nuanced challenges. In this paper, we introduce the Schur $p$-property and the strong Schur $p$-property for $0 < p \leq 1$, providing new tools to deepen the understanding of these spaces, and the Lipschitz free $p$-spaces in particular. Moreover, by developing an adapted version of the compact reduction principle, we prove that Lipschitz free $p$-spaces over discrete metric spaces possess the approximation property, thereby answering positively a question raised by Albiac et al. in arXiv:2005.06555v2.

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Fernando Albiac, José L. Ansorena, Jan Bíma, Marek Cúth. 2025-06-11. Lipschitz free $p$-spaces for $0<p<1$ in the light of the Schur $p$-property and the compact reduction. https://arxiv.org/abs/2506.09786

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