Continuous functionals for unbounded convergence in Banach lattices

Extension properties of order continuous functionals and applications to the theory of Banach lattices

Indagationes Mathematicae ◽

10.1016/0019-3577(94)90037-x ◽

1994 ◽

Vol 5 (1) ◽

pp. 107-118 ◽

Cited By ~ 5

Author(s):

Helmut H. Schaefer ◽

Xiao-Dong Zhang

Keyword(s):

Banach Lattices ◽

Continuous Functionals ◽

Order Continuous

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Compact Disjointness Preserving Polynomials on Quasi-Banach Lattices

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2021.124924 ◽

2021 ◽

pp. 124924

Author(s):

A.G. Kusraev ◽

Z.A. Kusraeva

Keyword(s):

Banach Lattices ◽

Disjointness Preserving

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On lattice-almost isometric copies of $$c_0(\Gamma )$$ and $$\ell _1(\Gamma )$$ in Banach lattices

Rendiconti del Circolo Matematico di Palermo (1952 -) ◽

10.1007/s12215-021-00620-y ◽

2021 ◽

Author(s):

Michael A. Rincón-Villamizar ◽

Andrés Fabián Leal-Archila

Keyword(s):

Banach Lattices

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Some applications of the complex interpolation method to Banach lattices

Journal d Analyse Mathématique ◽

10.1007/bf02791068 ◽

1979 ◽

Vol 35 (1) ◽

pp. 264-281 ◽

Cited By ~ 52

Author(s):

G. Pisier

Keyword(s):

Interpolation Method ◽

Banach Lattices ◽

Complex Interpolation

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Reflexivity in Banach lattices

Archiv der Mathematik ◽

10.1007/bf01202072 ◽

1994 ◽

Vol 63 (6) ◽

pp. 549-552 ◽

Cited By ~ 5

Author(s):

Santiago D�az ◽

Antonio Fern�ndez

Keyword(s):

Banach Lattices

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R.E. degrees of continuous functionals

Archive for Mathematical Logic ◽

10.1007/bf02023015 ◽

1983 ◽

Vol 23 (1) ◽

pp. 79-98 ◽

Cited By ~ 1

Author(s):

Dag Normann

Keyword(s):

Continuous Functionals

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Banach spaces with property (w)

Glasgow Mathematical Journal ◽

10.1017/s0017089500009769 ◽

1993 ◽

Vol 35 (2) ◽

pp. 207-217 ◽

Cited By ~ 2

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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