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 $$c_0$$ . For an infinite compact space K, the Banach space C(K) has the strong Gelfand–Phillips property iff C(K) is isomorphic to $$c_0$$ iff K is countable and has finite scattered height.
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