Diagonals of the Powers of an Operator on a Banach Lattice

1995 ◽  
pp. 223-273
Author(s):  
W. A. J. Luxemburg ◽  
B. de Pagter ◽  
A. R. Schep
Keyword(s):  
Banach Lattice

Tauberian theorems in a Banach lattice, with applications to the LP spaces

1954 ◽  
Vol 50 (2) ◽  
pp. 242-249
Author(s):  
D. C. J. Burgess
Keyword(s):  
Banach Space ◽  
Banach Lattice ◽  
Laplace Transforms ◽  
Tauberian Theorems ◽  
General Argument ◽  
Arbitrary Banach Space ◽  
Lp Spaces ◽  
Special Case

In a previous paper (2) of the author, there was given a treatment of Tauberian theorems for Laplace transforms with values in an arbitrary Banach space. Now, in § 2 of the present paper, this kind of technique is applied to the more special case of Laplace transforms with values in a Banach lattice, and investigations are made on what additional results can be obtained by taking into account the existence of an ordering relation in the space. The general argument is again based on Widder (5) to which frequent references are made.

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).

Space of operators acting from one banach lattice to another

1986 ◽  
Vol 34 (6) ◽  
pp. 2134-2137
Author(s):  
Yu. A. Abramovich
Keyword(s):  
Banach Lattice

scholarly journals Banach lattice sums with hereditary Fatou properties

2014 ◽  
Vol 50 (2) ◽  
pp. 271-282
Author(s):  
Mieczysław Mastyło ◽  
Enrique A. Sánchez-Pérez
Keyword(s):  
Banach Lattice ◽  
Lattice Sums

scholarly journals Projectivity of the free Banach lattice generated by a lattice

2019 ◽  
Vol 113 (5) ◽  
pp. 515-524 ◽  
Author(s):  
Antonio Avilés ◽  
José David Rodríguez Abellán
Keyword(s):  
Banach Lattice

scholarly journals Convergence in partially ordered groups

1973 ◽  
Vol 18 (3) ◽  
pp. 239-246
Author(s):  
Andrew Wirth
Keyword(s):  
Uniform Convergence ◽  
Banach Lattice ◽  
Order Convergence ◽  
Ordered Group ◽  
Partially Ordered ◽  
Partially Ordered Group ◽  
Ordered Groups ◽  
Integrally Closed ◽  
Relative Uniform Convergence ◽  
New Type

AbstractRelative uniform limits need not be unique in a non-archimedean partially ordered group, and order convergence need not imply metric convergence in a Banach lattice. We define a new type of convergence on partially ordered groups (R-convergence), which implies both the previous ones, and does not have these defects. Further R-convergence is equivalent to relative uniform convergence on divisible directed integrally closed partially ordered groups, and to order convergence on fully ordered groups.

scholarly journals The free Banach lattice generated by a Banach space

2018 ◽  
Vol 274 (10) ◽  
pp. 2955-2977 ◽  
Author(s):  
Antonio Avilés ◽  
José Rodríguez ◽  
Pedro Tradacete
Keyword(s):  
Banach Space ◽  
Banach Lattice

scholarly journals On orthogonally decomposable ordered Banach spaces

1984 ◽  
Vol 30 (3) ◽  
pp. 357-380 ◽  
Author(s):  
Sadayuki Yamamuro
Keyword(s):  
Banach Spaces ◽  
Banach Lattice ◽  
Order Structure ◽  
Duality Map ◽  
Ordered Banach Spaces

In a Banach lattice or the hermitian part of a C*-algebra, every element a admits a decomposition a = a+ − a− such that and N(−a) = ‖a−‖, where N is the canonical half-norm of the positive cones. In general ordered Banach spaces, this property is related to the order structure of the duality map and the metric projectability of the positive cones, and it turns out to be equivalent to an “orthogonal” decomposability.

scholarly journals Weak and unbounded order convergence in Banach lattices

1977 ◽  
Vol 24 (3) ◽  
pp. 312-319 ◽  
Author(s):  
A. W. Wickstead
Keyword(s):  
Weak Convergence ◽  
Banach Lattice ◽  
Vector Lattice ◽  
Banach Lattices ◽  
Order Convergence ◽  
The Relationship

AbstractA net (xy) in a vector lattice is unbounded order convergent (uo-convergent) to 0 if u ∧ |xv| order converges to 0 for all u ≧ 0. We consider, in a Banach lattice, the relationship between weak and uo-convergence. We characterise those Banach lattices in which weak convergence implies uo-convergence and those in which uo-convergence of a bounded net implies weak convergence. Finally we combine the results to characterise those Banach lattices in which weak and uo-convergence coincide for bounded nets.

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