Dehghani, Mohammad B.; Moshtaghioun, S. Mohammad On the \(p\)-Schur property of Banach spaces. (English) Zbl 1486.46008 Ann. Funct. Anal. 9, No. 1, 123-136 (2018). Summary: We introduce the notion of the \(p\)-Schur property (\(1\leq p\leq\infty\)) as a generalization of the Schur property of Banach spaces, and then we present a number of basic properties and some examples. We also study its relation with some geometric properties of Banach spaces, such as the Gelfand-Phillips property. Moreover, we verify some necessary and sufficient conditions for the \(p\)-Schur property of some closed subspaces of operator spaces. Cited in 7 Documents MSC: 46B03 Isomorphic theory (including renorming) of Banach spaces 47B07 Linear operators defined by compactness properties 46B28 Spaces of operators; tensor products; approximation properties Keywords:Gelfand-Phillips property; Schur property; weakly \(p\)-compact set; weakly \(p\)-convergent sequence PDFBibTeX XMLCite \textit{M. B. Dehghani} and \textit{S. M. Moshtaghioun}, Ann. Funct. Anal. 9, No. 1, 123--136 (2018; Zbl 1486.46008) Full Text: DOI Euclid