Majorization for Compact and Weakly Compact Polynomials on Banach Lattices

2019 ◽  
pp. 339-348 ◽  
Author(s):  
Yongjin Li ◽  
Qingying Bu
Keyword(s):  
Banach Lattices ◽  
Weakly Compact

scholarly journals Banach spaces with property (w)

1993 ◽  
Vol 35 (2) ◽  
pp. 207-217 ◽  
Author(s):  
Denny H. Leung
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Banach Lattice ◽  
Banach Lattices ◽  
Weakly Compact ◽  
Type Spaces

A Banach space E is said to have Property (w) if every operator from E into E' is weakly compact. This property was introduced by E. and P. Saab in [9]. They observe that for Banach lattices, Property (w) is equivalent to Property (V*), which in turn is equivalent to the Banach lattice having a weakly sequentially complete dual. Thus the following question was raised in [9].Does every Banach space with Property (w) have a weakly sequentially complete dual, or even Property (V*)?In this paper, we give two examples, both of which answer the question in the negative. Both examples are James type spaces considered in [1]. They both possess properties stronger than Property (w). The first example has the property that every operator from the space into the dual is compact. In the second example, both the space and its dual have Property (w). In the last section we establish some partial results concerning the problem (also raised in [9]) of whether (w) passes from a Banach space E to C(K, E).

scholarly journals Some properties of positive weak Dunford-Pettis operators on Banach lattices

2009 ◽  
Vol 42 (4) ◽  
Author(s):  
Belmesnaoui Aqzzouz ◽  
Khalid Bourass
Keyword(s):  
Banach Lattices ◽  
Weakly Compact

AbstractWe characterize Banach lattices for which each positive weak Dunford-Pettis operator is weakly compact. As consequences, we obtain some interesting results on reflexive Banach lattices.

On the structure of non-weakly compact operators on Banach lattices

1981 ◽  
Vol 257 (3) ◽  
pp. 317-334 ◽  
Author(s):  
T. Figiel ◽  
N. Ghoussoub ◽  
W. B. Johnson
Keyword(s):  
Compact Operators ◽  
Banach Lattices ◽  
Weakly Compact ◽  
Weakly Compact Operators

About b-weakly compact operators on Banach lattices

2012 ◽  
Vol 61 (3) ◽  
pp. 355-360
Author(s):  
Khalid Bouras ◽  
Abdelmonaim El Kaddouri ◽  
Jawad H’michane ◽  
Mohammed Moussa
Keyword(s):  
Compact Operators ◽  
Banach Lattices ◽  
Weakly Compact ◽  
Weakly Compact Operators
Sign in / Sign up

Export Citation Format

Share Document