Displaying similar documents to “On the lower semi-continuity of the set valued metric projection.”

Domination by positive Banach-Saks operators

Julio Flores, César Ruiz (2006)

Studia Mathematica

Similarity:

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.

Factorization and domination of positive Banach-Saks operators

Julio Flores, Pedro Tradacete (2008)

Studia Mathematica

Similarity:

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.

Generalized Alexandroff Duplicates and CD 0(K) spaces

Mert Çaglar, Zafer Ercan, Faruk Polat (2006)

Open Mathematics

Similarity:

We define and investigateCD Σ,Γ(K, E)-type spaces, which generalizeCD 0-type Banach lattices introduced in [1]. We state that the space CD Σ,Γ(K, E) can be represented as the space of E-valued continuous functions on the generalized Alexandroff Duplicate of K. As a corollary we obtain the main result of [6, 8].

The lattice copies of ℓ 1 in Banach lattices

Marek Wójtowicz (2001)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

It is known that a Banach lattice with order continuous norm contains a copy of ℓ 1 if and only if it contains a lattice copy of ℓ 1 . The purpose of this note is to present a more direct proof of this useful fact, which extends a similar theorem due to R.C. James for Banach spaces with unconditional bases, and complements the c 0 - and ℓ ∞ -cases considered by Lozanovskii, Mekler and Meyer-Nieberg.