On quantitative Gelfand-Phillips property and Phillips property

0559727 - MÚ 2023 RIV US eng J - Journal Article
Chen, D. - Kania, Tomasz - Ruan, Y.
On quantitative Gelfand-Phillips property and Phillips property.
Journal of Mathematical Analysis and Applications. Roč. 516, č. 2 (2022), č. článku 126532. ISSN 0022-247X. E-ISSN 1096-0813
Institutional support: RVO:67985840
Keywords : limited sets * Phillips property * quantitative Dunford-Pettis property * quantitative Gelfand-Phillips property * weakly precompact
OECD category: Pure mathematics
Impact factor: 1.3, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.jmaa.2022.126532

Possible quantifications of well-known relationships among four classes of sets-relatively norm compact, limited, relatively weakly compact and weakly precompact ones, are investigated. We introduce and investigate quantitative versions of the Gelfand-Phillips property. As applications, we quantify the Phillips property and estimate possible values of the quantities measuring the property. Finally, we prove that c0 enjoys a quantitative version of the Phillips property.
Permanent Link: https://hdl.handle.net/11104/0332935