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

Taras Banakh; Saak Gabriyelyan

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

Functional Analysis 2021-10-18 v1 General Topology

Authors: Taras Banakh , Saak Gabriyelyan

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.

Keywords

Banach space Gelfand-Phillips property strong Gelfand-Phillips property embedding into c_0 C(K) space scattered height

Cite

@article{arxiv.2110.07991,
  title  = {Banach spaces with the (strong) Gelfand--Phillips property},
  author = {Taras Banakh and Saak Gabriyelyan},
  journal= {arXiv preprint arXiv:2110.07991},
  year   = {2021}
}

Comments

10 pages. arXiv admin note: substantial text overlap with arXiv:2003.06764

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

Abstract

Keywords

Cite

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