A characterization of weakly sequentially complete Banach lattices

1985 ◽  
Vol 190 (3) ◽  
pp. 379-385 ◽  
Author(s):  
V. Caselles
Keyword(s):  
Banach Lattices

scholarly journals A characterization of discrete Banach lattices with order continuous norms

1988 ◽  
Vol 104 (1) ◽  
pp. 197-197 ◽  
Author(s):  
Witold Wnuk
Keyword(s):  
Banach Lattices ◽  
Order Continuous

scholarly journals Cone characterization of reflexive Banach lattices

1995 ◽  
Vol 37 (1) ◽  
pp. 65-67 ◽  
Author(s):  
Ioannis A. Polyrakis
Keyword(s):  
Banach Lattice ◽  
Normal Cone ◽  
Banach Lattices

AbstractWe prove that a Banach lattice X is reflexive if and only if X+ does not contain a closed normal cone with an unbounded closed dentable base.

Interpolation of weighted Banach lattices. A characterization of relatively decomposable Banach lattices

2003 ◽  
Vol 165 (787) ◽  
pp. 0-0 ◽  
Author(s):  
Michael Cwikel ◽  
Per G. Nilsson ◽  
Gideon Schechtman
Keyword(s):  
Banach Lattices

scholarly journals Geometric Characterization of Injective Banach Lattices

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 250
Author(s):  
Anatoly Kusraev ◽  
Semën Kutateladze
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Banach Spaces ◽  
Set Theory ◽  
Banach Lattice ◽  
Dual Space ◽  
Banach Lattices ◽  
Transfer Principle ◽  
Ordered Banach Spaces

This is a continuation of the authors’ previous study of the geometric characterizations of the preduals of injective Banach lattices. We seek the properties of the unit ball of a Banach space which make the space isometric or isomorphic to an injective Banach lattice. The study bases on the Boolean valued transfer principle for injective Banach lattices. The latter states that each such lattice serves as an interpretation of an AL-space in an appropriate Boolean valued model of set theory. External identification of the internal Boolean valued properties of the corresponding AL-spaces yields a characterization of injective Banach lattices among Banach spaces and ordered Banach spaces. We also describe the structure of the dual space and present some dual characterization of injective Banach lattices.

scholarly journals The Schur and (weak) Dunford-Pettis properties in Banach lattices

2002 ◽  
Vol 73 (2) ◽  
pp. 251-278 ◽  
Author(s):  
Anna Kamińska ◽  
Mieczysław Mastyło
Keyword(s):  
Orlicz Spaces ◽  
Sufficient Conditions ◽  
Complete Characterization ◽  
Sequence Spaces ◽  
Banach Lattices ◽  
Schur Property ◽  
Atomic Measure ◽  
Orlicz Sequence Spaces ◽  
Necessary And Sufficient

AbstractWe study the Schur and (weak) Dunford-Pettis properties in Banach lattices. We show that l1, c0 and l∞ are the only Banach symmetric sequence spaces with the weak Dunford-Pettis property. We also characterize a large class of Banach lattices without the (weak) Dunford-Pettis property. In MusielakOrlicz sequence spaces we give some necessary and sufficient conditions for the Schur property, extending the Yamamuro result. We also present a number of results on the Schur property in weighted Orlicz sequence spaces, and, in particular, we find a complete characterization of this property for weights belonging to class ∧. We also present examples of weighted Orlicz spaces with the Schur property which are not L1-spaces. Finally, as an application of the results in sequence spaces, we provide a description of the weak Dunford-Pettis and the positive Schur properties in Orlicz spaces over an infinite non-atomic measure space.

A characterization of positively decomposable non-linear maps between Banach lattices

Positivity ◽  
2008 ◽  
Vol 12 (3) ◽  
pp. 495-502 ◽  
Author(s):  
William A. Feldman ◽  
Pramod Singh
Keyword(s):  
Banach Lattices ◽  
Linear Maps ◽  
Non Linear

scholarly journals A local characterization of Banach lattices with order continuous norm

1976 ◽  
Vol 58 (2) ◽  
pp. 101-128 ◽  
Author(s):  
S. Bernau ◽  
H. Lacey
Keyword(s):  
Banach Lattices ◽  
Order Continuous Norm ◽  
Continuous Norm ◽  
Local Characterization ◽  
Order Continuous

scholarly journals A characterization of dual Banach lattices

1989 ◽  
Vol 92 (1) ◽  
pp. 35-47 ◽  
Author(s):  
V. Caselles
Keyword(s):  
Banach Lattices
Sign in / Sign up

Export Citation Format

Share Document