Scholarlink

<p>The geometric analysis of non-locally convex quasi-Banach spaces presents rich and nuanced challenges. In this paper, we introduce the Schur <i>p</i>-property and the strong Schur <i>p</i>-property for <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(0 &lt; p \le 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>&lt;</mo> <mi>p</mi> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, providing new tools to deepen the understanding of these spaces, and the Lipschitz free <i>p</i>-spaces in particular. Moreover, by developing an adapted version of the compact reduction principle, we prove that Lipschitz free <i>p</i>-spaces over discrete metric spaces possess the approximation property, thereby answering positively a question raised by Albiac et al. in [<CitationRef CitationID="CR4">4</CitationRef>].</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Lipschitz free \(\varvec{p}\)-spaces for \(\varvec{0 in the light of the Schur \(\varvec{p}\)-property and the compact reduction

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年12月22日

查看全文
  • Fernando Albiac,
  • José L. Ansorena,
  • Jan Bíma,
  • Marek Cúth

摘要

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 \(0 < p \le 1\) 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 [4].