Scholarlink

<p>Continuing with the study of approximately ultrahomogeneous and Fraïssé Banach spaces introduced by V. Ferenczi, J. López-Abad, B. Mbombo and S. Todorcevic, we define formally weaker and in some aspects more natural properties of Banach spaces which we call Almost ultrahomogeneity and the Almost Fraïssé Property. We obtain relations between these different homogeneity properties of a space <i>E</i> and relate them to certain pseudometrics on the class Age(<i>E</i>) of finite-dimensional subspaces of <i>E</i>. We prove that ultrapowers of an almost Fraïssé Banach space are ultrahomogeneous. We also study two properties called finitely isometrically extensible and almost finitely isometrically extensible, respectively, and prove that approximately ultrahomogeneous reflexive Banach spaces are finitely isometrically extensible.</p><p>Finally, we study oligomorphy in Banach spaces, and give a proof that a Banach space is Fraïssé if and only if it is approximately ultrahomogeneous and oligomorphic.</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

Almost Fraïssé Banach spaces

  • 期刊论文

  • 发表日期：

    2025年7月30日

查看全文
  • Valentin Ferenczi,
  • Michael A. Rincón-Villamizar

摘要

Continuing with the study of approximately ultrahomogeneous and Fraïssé Banach spaces introduced by V. Ferenczi, J. López-Abad, B. Mbombo and S. Todorcevic, we define formally weaker and in some aspects more natural properties of Banach spaces which we call Almost ultrahomogeneity and the Almost Fraïssé Property. We obtain relations between these different homogeneity properties of a space E and relate them to certain pseudometrics on the class Age(E) of finite-dimensional subspaces of E. We prove that ultrapowers of an almost Fraïssé Banach space are ultrahomogeneous. We also study two properties called finitely isometrically extensible and almost finitely isometrically extensible, respectively, and prove that approximately ultrahomogeneous reflexive Banach spaces are finitely isometrically extensible.

Finally, we study oligomorphy in Banach spaces, and give a proof that a Banach space is Fraïssé if and only if it is approximately ultrahomogeneous and oligomorphic.