Generalized Alexandroff Duplicates and CD 0(K) spaces

Mert Çaglar; Zafer Ercan; Faruk Polat

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Displaying similar documents to “Generalized Alexandroff Duplicates and CD 0(K) spaces”

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CONTENTS§ 1. Introduction.................................................................................................... 5§ 2. Basic development............................................................................................... 8§ 3. Some elementarily equivalent spaces............................................................. 11§ 4. Elementary characterizations of some familiar spaces................................ 13§ 5. First order properties of C(X).................................................................................

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For a locally compact Hausdorff space K and a Banach space X we denote by C₀(K,X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Γ an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C₀(Γ,X) and C₀(K,X) is greater than or equal to 2n + 1. We also show that the...

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Factorization and domination of positive Banach-Saks operators

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It is proved that every positive Banach-Saks operator T: E → F between Banach lattices E and F factors through a Banach lattice with the Banach-Saks property, provided that F has order continuous norm. By means of an example we show that this order continuity condition cannot be removed. In addition, some domination results, in the Dodds-Fremlin sense, are obtained for the class of Banach-Saks operators.

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Witold Wnuk (1989)

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This note contains a short proof of the equivalence of the Schur and Dunford-Pettis properties in the class of discrete KB-spaces. We also present an operator characterization of the Schur property (Theorem 2) and we notice that Banach lattices which band hereditary l1 coincide with Banach lattices having the Schur property. (This characterization is due to Popa (1977)). Moreover, the paper offers examples of Banach lattices with the positive Schur property and without the Schur property...

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