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

A note on Riesz spaces with property- b

Ş. Alpay, B. Altin, C. Tonyali (2006)

Czechoslovak Mathematical Journal

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We study an order boundedness property in Riesz spaces and investigate Riesz spaces and Banach lattices enjoying this property.

First order topology

C.W. Henson, C.G. Jockusch, Jr., L.A. Rubel, G. Takeuti

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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).................................................................................

Domination by positive Banach-Saks operators

Julio Flores, César Ruiz (2006)

Studia Mathematica

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Given a positive Banach-Saks operator T between two Banach lattices E and F, we give sufficient conditions on E and F in order to ensure that every positive operator dominated by T is Banach-Saks. A counterexample is also given when these conditions are dropped. Moreover, we deduce a characterization of the Banach-Saks property in Banach lattices in terms of disjointness.

How far is C₀(Γ,X) with Γ discrete from C₀(K,X) spaces?

Leandro Candido, Elói Medina Galego (2012)

Fundamenta Mathematicae

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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...

Factorization and domination of positive Banach-Saks operators

Julio Flores, Pedro Tradacete (2008)

Studia Mathematica

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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.

Some characterizations of Banach lattices with the Schur property.

Witold Wnuk (1989)

Revista Matemática de la Universidad Complutense de Madrid

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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...