Semenov, E. M.; Sukochev, F. A. The Banach-Saks property. (Russian) Zbl 1299.46014 Vladikavkaz. Mat. Zh. 7, No. 3, 64-70 (2005). From the introduction: This is a survey on the Banach-Saks property and Banach-Saks \(p\)-property. The concept of the Banach-Saks index is introduced. The emphasis is on rearrangement-invariant spaces. It is shown that the Banach-Saks property and the Banach-Saks \(p\)-property are closely related to other geometric properties of Banach spaces (such as space type, \(p\)-convexity, Boyd indices). As an example, Orlicz spaces and \(L_{p, q}\) are considered. MSC: 46B03 Isomorphic theory (including renorming) of Banach spaces 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46-02 Research exposition (monographs, survey articles) pertaining to functional analysis Keywords:weakly convergent sequence; subsequence; sequence space PDFBibTeX XMLCite \textit{E. M. Semenov} and \textit{F. A. Sukochev}, Vladikavkaz. Mat. Zh. 7, No. 3, 64--70 (2005; Zbl 1299.46014) Full Text: MNR