Banach spaces with the (strong) Gelfand–Phillips property

T. Banakh, S. Gabriyelyan

Research output: Contribution to journalArticlepeer-review

Abstract

Several new characterizations of the Gelfand–Phillips property are given. We define a strong version of the Gelfand–Phillips property and prove that a Banach space has this stronger property iff it embeds into c. For an infinite compact space K, the Banach space C(K) has the strong Gelfand–Phillips property iff C(K) is isomorphic to c iff K is countable and has finite scattered height.

Original languageEnglish
Article number24
JournalBanach Journal of Mathematical Analysis
Volume16
Issue number2
DOIs
StatePublished - 1 Apr 2022

Keywords

  • Banach space
  • Gelfand–Phillips property
  • Strong Gelfand–Phillips property

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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