scholarly journals Bases in the space of regular multilinear operators on Banach lattices

2018 ◽  
Vol 457 (1) ◽  
pp. 803-821 ◽  
Author(s):  
Donghai Ji ◽  
Khazhak Navoyan ◽  
Qingying Bu
Keyword(s):  
Banach Lattices ◽  
Multilinear Operators

Abstract M- and Abstract L-Spaces of Polynomials on Banach Lattices

2015 ◽  
Vol 58 (3) ◽  
pp. 617-629 ◽  
Author(s):  
Qingying Bu ◽  
Gerard Buskes ◽  
Yongjin Li
Keyword(s):  
Bounded Variation ◽  
Unconditional Basis ◽  
Banach Lattices ◽  
Multilinear Operators

AbstractIn this paper we use the norm of bounded variation to study multilinear operators and polynomials on Banach lattices. As a result, we obtain when all continuous multilinear operators and polynomials on Banach lattices are regular. We also provide new abstract M- and abstract L-spaces of multilinear operators and polynomials and generalize all the results by Grecu and Ryan, from Banach lattices with an unconditional basis to all Banach lattices.

scholarly journals On the positive Dimant strongly $p$-summing multilinear operators

2020 ◽  
Vol 12 (2) ◽  
pp. 401-411
Author(s):  
A. Bougoutaia ◽  
A. Belacel ◽  
H. Hamdi
Keyword(s):  
Banach Lattices ◽  
Multilinear Operators ◽  
New Class ◽  
Interesting Class

In 2003, Dimant V. has defined and studied the interesting class of strongly $p$-summing multilinear operators. In this paper, we introduce and study a new class of operators between two Banach lattices, where we extend the previous notion to the positive framework, and prove, among other results, the domination, inclusion and composition theorems. As consequences, we investigate some connections between our class and other classes of operators, such as duality and linearization.

Closed surjective ideals of multilinear operators and interpolation

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
Antonio Manzano ◽  
Pilar Rueda ◽  
Enrique A. Sánchez-Pérez
Keyword(s):  
Multilinear Operators ◽  
Ideals Of Multilinear Operators

Reflexivity in Banach lattices

1994 ◽  
Vol 63 (6) ◽  
pp. 549-552 ◽  
Author(s):  
Santiago D�az ◽  
Antonio Fern�ndez
Keyword(s):  
Banach Lattices

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).

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