共查询到20条相似文献,搜索用时 11 毫秒
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Witold Wnuk 《Positivity》2013,17(3):759-773
The paper contains several characterizations of Banach lattices $E$ with the dual positive Schur property (i.e., $0 \le f_n \xrightarrow {\sigma (E^*,E)} 0$ implies $\Vert f_n\Vert \rightarrow 0$ ) and various examples of spaces having this property. We also investigate relationships between the dual positive Schur property, the positive Schur property, the positive Grothendieck property and the weak Dunford–Pettis property. 相似文献
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A map between Banach lattices E and F is called positively decomposable if Tf = g
1 + g
2 for f, g
1, g
2 positive and g
1 and g
2 disjoint implies there exist disjoint positive elements f
1 and f
2 each less than f with the property that Tf
1 = g
1 and Tf
2 = g
2. Recently, the positive decomposability of linear Carleman operators on Banach lattices were characterized using disjointness
condition of images of the approximate atoms. This note provides an extension of the characterization for a class of non-linear
maps. Further, disjointness preserving maps are studied.
相似文献
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Manuel González Antonio Martínez-Abejón 《Journal of Mathematical Analysis and Applications》2007,327(2):816-828
A local dual of a Banach space X is a closed subspace of X∗ that satisfies the properties that the principle of local reflexivity assigns to X as a subspace of X∗∗. Here we introduce a technical property which characterizes the local dual spaces of a Banach space and allows us to show new examples of local dual spaces. 相似文献
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E. V. Tokarev 《Functional Analysis and Its Applications》1981,15(2):150-151
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《Journal of Functional Analysis》2023,284(10):109888
The construction of the free Banach lattice generated by a real Banach space is extended to the complex setting. It is shown that for every complex Banach space E there is a complex Banach lattice containing a linear isometric copy of E and satisfying the following universal property: for every complex Banach lattice , every operator admits a unique lattice homomorphic extension with . The free complex Banach lattice is shown to have analogous properties to those of its real counterpart. However, examples of non-isomorphic complex Banach spaces E and F can be given so that and are lattice isometric. The spectral theory of induced lattice homomorphisms on is also explored. 相似文献
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Reflexivity in Banach lattices 总被引:1,自引:0,他引:1
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In this paper we present a counterexample of compact domination compact operator T such that |T'| is compact but |T| need not compact. 相似文献
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A. G. Kusraev 《Positivity》2010,14(4):785-799
The aim of this paper is to outline a portion of the theory of liftable bundles of Banach lattices and to give some applications to representation of dominated operators. 相似文献
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Peter Ørno 《Israel Journal of Mathematics》1974,19(3):264-265
Let Λ1 and Λ2 be infinte-dimensional, Banach lattices such thatc o is not finitely representable in Λ2. Then the bounded linear operators from Λ1 to Λ2 form a lattice if and only if Λ1 is an abstract AL space. 相似文献
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A result of Aliprantis and Burkinshaw shows that weakly compact operators from an AL-space into a KB-space have a weakly compact modulus. Groenewegen characterised the largest class of range spaces for which this remains true whenever the domain is an AL-space and Schmidt proved a dual result. Both of these authors used vector-valued integration in their proofs. We give elementary proofs of both results and also characterise the largest class of domains for which the conclusion remains true whenever the range space is a KB-space. We conclude by studying the order structure of spaces of weakly compact operators between Banach lattices to prove results analogous to earlier results of one of the authors for spaces of compact operators.
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Tadeusz Figiel William B. Johnson Aleksander Pe?czyński 《Israel Journal of Mathematics》2011,183(1):199-231
The notion of the bounded approximation property = BAP (resp. the uniform approximation property = UAP) of a pair [Banach space, its subspace] is used to prove that if X is a ℒ
∞-space, Y a subspace with the BAP (resp. UAP), then the quotient X/Y has the BAP (resp. UAP). If Q: X → Z is a surjection, X is a ℒ
1-space and Z is a ℒ
p
-space (1 ≤ p ≤ ∞), then ker Q has the UAP. A complemented subspace of a weakly sequentially complete Banach lattice has the separable complementation property = SCP.
A criterion for a space with GL-l.u.st. to have the SCP is given. Spaces which are quotients of weakly sequentially complete
lattices and are uncomplemented in their second duals are studied. Examples are given of spaces with the SCP which have subspaces
that fail the SCP. The results are applied to spaces of measures on a compact Abelian group orthogonal to a fixed Sidon set
and to Sobolev spaces of functions of bounded variation on ℝ
n
. 相似文献
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