scholarly journals The positive polynomial Schur property in Banach lattices

2020 ◽  
pp. 1
Author(s):  
Geraldo Botelho ◽  
José Lucas P. Luiz
Keyword(s):  
Banach Lattices ◽  
Schur Property ◽  
Positive Polynomial

A Perron-Frobenius theorem for positive polynomial operators in Banach lattices

Positivity ◽  
2009 ◽  
Vol 13 (4) ◽  
pp. 709-716 ◽  
Author(s):  
Bui The Anh ◽  
Nguyen Khoa Son ◽  
Duong Dang Xuan Thanh
Keyword(s):  
Banach Lattices ◽  
Frobenius Theorem ◽  
Positive Polynomial ◽  
Polynomial Operators

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.

scholarly journals A note on the positive Schur property

1989 ◽  
Vol 31 (2) ◽  
pp. 169-172 ◽  
Author(s):  
Witold Wnuk
Keyword(s):  
Positive Operators ◽  
Banach Lattices ◽  
Schur Property ◽  
The Difference

The purpose of this note is to characterize those Banach lattices (E, ∥·∥) which have the property:an operator T: E → c0 is a Dunford-Pettis operator if and only if T is regular (*)(i.e., T is the difference of two positive operators). Our characterization generalizes a theorem recently proved by Holub [6] and Gretsky and Ostroy [4], who have remarked that the space L1[0, 1] has the property (*). The main result presented here is the following theorem.

The strong Schur property in Banach lattices

Positivity ◽  
2008 ◽  
Vol 13 (2) ◽  
pp. 435-441 ◽  
Author(s):  
Witold Wnuk
Keyword(s):  
Banach Lattices ◽  
Schur Property

scholarly journals Weak sequential convergence in the dual of compact operators between Banach lattices

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 723-728
Author(s):  
Halimeh Ardakani ◽  
Modarres Sadegh ◽  
Mohammad Moshtaghiouna
Keyword(s):  
Unit Ball ◽  
Closed Subspace ◽  
Compact Operators ◽  
Banach Lattices ◽  
Closed Unit Ball ◽  
Schur Property ◽  
Sequential Convergence ◽  
Point Evaluations

For several Banach lattices E and F, if K(E,F) denotes the space of all compact operators from E to F, under some conditions on E and F, it is shown that for a closed subspace M of K(E,F), M* has the Schur property if and only if all point evaluations M1(x) = {Tx : T ? M1} and ~M1(y*) = {T* y* : T ? M1} are relatively norm compact, where x ? E, y* ? F* and M1 is the closed unit ball of M.

scholarly journals On the dual positive Schur property in Banach lattices

Positivity ◽  
2012 ◽  
Vol 17 (3) ◽  
pp. 759-773 ◽  
Author(s):  
Witold Wnuk
Keyword(s):  
Banach Lattices ◽  
Schur Property
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