On the structure of solutions sets of differential and integral equations in Banach spaces
Stanisław Szufla (1977)
Annales Polonici Mathematici
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Displaying similar documents to “A remark on a theorem of Banach”
On the structure of solutions sets of differential and integral equations in Banach spaces
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This paper studies the Banach-Saks property in rearrangement invariant spaces on the positive half-line. A principal result of the paper shows that a separable rearrangement invariant space E with the Fatou property has the Banach-Saks property if and only if E has the Banach-Saks property for disjointly supported sequences. We show further that for Orlicz and Lorentz spaces, the Banach-Saks property is equivalent to separability although the separable parts of some Marcinkiewicz spaces...
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An amalgamation of the Banach spaces associated with James and Schreier, Part I: Banach-space structure
Alistair Bird, Niels Jakob Laustsen (2010)
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We create a new family of Banach spaces, the James-Schreier spaces, by amalgamating two important classical Banach spaces: James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. We then investigate the properties of these James-Schreier spaces, paying particular attention to how key properties of their 'ancestors' (that is, the James space and the Schreier space) are expressed in them. Our main...