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The Banach-Saks property. (Russian) Zbl 1299.46014

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
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