Locally convex spaces with the strong Gelfand–Phillips property

Taras Banakh, Saak Gabriyelyan

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We introduce the strong Gelfand–Phillips property for locally convex spaces and give several characterizations of this property. We characterize the strong Gelfand–Phillips property among locally convex spaces admitting a stronger Banach space topology. If CT(X) is a space of continuous functions on a Tychonoff space X, endowed with a locally convex topology T between the pointwise topology and the compact-open topology, then: (a) the space CT(X) has the strong Gelfand–Phillips property iff X contains a compact countable subspace K⊆ X of finite scattered height such that for every functionally bounded set B⊆ X the complement B\ K is finite, (b) the subspace CTb(X) of CT(X) consisting of all bounded functions on X has the strong Gelfand–Phillips property iff X is a compact countable space of finite scattered height.

Original languageEnglish
Article number27
JournalAnnals of Functional Analysis
Volume14
Issue number2
DOIs
StatePublished - 1 Apr 2023

Keywords

  • Banach space
  • function space
  • Locally convex space
  • The strong Gelfand–Phillips property

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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