×

On the \(p\)-Schur property of Banach spaces. (English) Zbl 1486.46008

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.

MSC:

46B03 Isomorphic theory (including renorming) of Banach spaces
47B07 Linear operators defined by compactness properties
46B28 Spaces of operators; tensor products; approximation properties
PDFBibTeX XMLCite
Full Text: DOI Euclid