Banach spaces with the (strong) Gelfand–Phillips property

T. Banakh; S. Gabriyelyan

doi:10.1007/s43037-022-00179-5

Banach spaces with the (strong) Gelfand–Phillips property

T. Banakh, S. Gabriyelyan

Department of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Article number	24
Journal	Banach Journal of Mathematical Analysis
Volume	16
Issue number	2
DOIs	https://doi.org/10.1007/s43037-022-00179-5
State	Published - 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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10.1007/s43037-022-00179-5

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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.",

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N2 - 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.

AB - 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.

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Banach spaces with the (strong) Gelfand–Phillips property

Abstract

Keywords

ASJC Scopus subject areas

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