Locally convex spaces with the strong Gelfand–Phillips property

Taras Banakh, Saak Gabriyelyan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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
Issue number2
StatePublished - 17 Jan 2023


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

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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