2025/06/11 by Albiac, Fernando, Ansorena, José L., Bíma, Jan +1
#46B03 (Primary) #46B07 #46B08 #46B10 #46B15 #46B20 #46B25 #46B42 #46E30 #46E40 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2506.09786
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 ≤ 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.