A description of relatively (p; r)-compact sets

  • Kati Ain Faculty of Mathematics and Computer Science, Tartu University, J. Liivi 2, 50409 Tartu, Estonia
  • Eve Oja Faculty of Mathematics and Computer Science, Tartu University, J. Liivi 2, 50409 Tartu, Estonia; Estonian Academy of Sciences, Kohtu 6, 10130 Tallinn, Estonia
Keywords: Banach spaces, (p; r)-compactness, (p; r)-null sequences

Abstract

We introduce the notion of (p; r)-null sequences in a Banach space and we prove a Grothendieck-like result: a subset of a Banach space is relatively (p; r)-compact if and only if it is contained in the closed convex hull of a (p; r)-null sequence. This extends a recent description of relatively p-compact sets due to Delgado and Piñeiro, providing to it an alternative straightforward proof.

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Published
2020-09-25
Section
Articles