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 |
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Article number | 24 |
Journal | Banach Journal of Mathematical Analysis |
Volume | 16 |
Issue number | 2 |
DOIs | |
State | Published - 1 Apr 2022 |
Keywords
- Banach space
- Gelfand–Phillips property
- Strong Gelfand–Phillips property
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory