On quantitative Gelfand-Phillips property and Phillips property (Q2674868)

This paper concerns quantifications of some relationships among classes of sets of a Banach space \(X\). These classes include relatively norm compact, limited, relatively weakly compact, and weakly compact sets. Quantitative versions of the Gelfand-Phillips and Phillips properties are also introduced and investigated. As a consequence, it is proved that \(c_0\) enjoys the 1-Phillips property.