OnC 0-semigroups of lattice homomorphisms on a Banach lattice

1978 ◽  
Vol 164 (1) ◽  
pp. 69-80 ◽  
Author(s):  
Manfred Wolff
Keyword(s):  
Banach Lattice ◽  
Lattice Homomorphisms

scholarly journals Amalgamation and Injectivity in Banach Lattices

2021 ◽  
Author(s):  
Antonio Avilés ◽  
Pedro Tradacete
Keyword(s):  
Banach Lattice ◽  
Amalgamation Property ◽  
Banach Lattices ◽  
Lattice Construction ◽  
Lattice Homomorphisms

Abstract We study distinguished objects in the category $\mathcal{B}\mathcal{L}$ of Banach lattices and lattice homomorphisms. The free Banach lattice construction introduced by de Pagter and Wickstead [ 8] generates push-outs, and combining this with an old result of Kellerer [ 17] on marginal measures, the amalgamation property of Banach lattices is established. This will be the key tool to prove that $L_1([0,1]^{\mathfrak{c}})$ is separably $\mathcal{B}\mathcal{L}$-injective, as well as to give more abstract examples of Banach lattices of universal disposition for separable sublattices. Finally, an analysis of the ideals on $C(\Delta ,L_1)$, which is a separably universal Banach lattice as shown by Leung et al. [ 21], allows us to conclude that separably $\mathcal{B}\mathcal{L}$-injective Banach lattices are necessarily non-separable.

scholarly journals Free and projective Banach lattices

2015 ◽  
Vol 145 (1) ◽  
pp. 105-143 ◽  
Author(s):  
Ben de Pagter ◽  
Anthony W. Wickstead
Keyword(s):  
Finite Number ◽  
Banach Lattice ◽  
Banach Lattices ◽  
Closed Ideal ◽  
Lattice Homomorphism ◽  
Linear Lattice ◽  
Fundamental Properties ◽  
Number Of Generators ◽  
Lattice Homomorphisms

We define and prove the existence of free Banach lattices in the category of Banach lattices and contractive lattice homomorphisms, and establish some of their fundamental properties. We give much more detailed results about their structure in the case when there are only a finite number of generators, and give several Banach lattice characterizations of the number of generators being, respectively, one, finite or countable. We define a Banach lattice P to be projective if, whenever X is a Banach lattice, J is a closed ideal in X, Q : X → X/J is the quotient map, T : P → X/J is a linear lattice homomorphism and ε > 0, there exists a linear lattice homomorphism : P → X such that T = Q º and ∥∥ ≤ (1 + ε)∥T∥. We establish the connection between projective Banach lattices and free Banach lattices, describe several families of Banach lattices that are projective and prove that some are not.

Extension of Vector Lattice Homomorphisms

1986 ◽  
Vol s2-33 (3) ◽  
pp. 516-524 ◽  
Author(s):  
S. J. Bernau
Keyword(s):  
Vector Lattice ◽  
Lattice Homomorphisms

Factorization by lattice homomorphisms

1984 ◽  
Vol 185 (4) ◽  
pp. 567-571 ◽  
Author(s):  
Wolfgang Arendt
Keyword(s):  
Lattice Homomorphisms

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

Sums and extensions of vector lattice homomorphisms

1992 ◽  
Vol 27 (1-2) ◽  
pp. 33-45 ◽  
Author(s):  
S. J. Bernau
Keyword(s):  
Vector Lattice ◽  
Lattice Homomorphisms
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