# Banach spaces with the (strong) Gelfand--Phillips property

@inproceedings{Banakh2021BanachSW, title={Banach spaces with the (strong) Gelfand--Phillips property}, author={Taras O. Banakh and Saak Gabriyelyan}, year={2021} }

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 c0. For an infinite compact space K, the Banach space C(K) has the strong Gelfand–Phillips property iff C(K) is isomorphic to c0 iff K is countable and has finite scattered height.

## 3 Citations

Locally convex spaces with the strong Gelfand-Phillips property

- Mathematics
- 2021

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…

The Gelfand-Phillips property for locally convex spaces

- Mathematics
- 2021

We extend the well-known Gelfand–Phillips property for Banach spaces to locally convex spaces, defining a locally convex space E to be Gelfand–Phillips if every limited set in E is precompact in the…

A simple Efimov space with sequentially-nice space of probability measures

- Mathematics
- 2021

Under Jensen’s diamond principle ♦, we construct a simple Efimov space K whose space of nonatomic probability measures Pna(K) is first-countable and sequentially compact. These two properties of…

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Under Jensen’s diamond principle ♦, we construct a simple Efimov space K whose space of nonatomic probability measures Pna(K) is first-countable and sequentially compact. These two properties of…

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