首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper we study the positive approximation property (p.a.p.) of Banach lattices. The main results give some characterizations of the p.a.p. and the bounded p.a.p. Some perturbation results on positive operators, which are of interest in other contexts, too, are proved.  相似文献   

2.
Witold Wnuk 《Positivity》2009,13(2):435-441
We prove that in the class of discrete Banach lattices the strong Schur property is equivalent to the disjoint strong Schur property (Theorem 3.1). Roughly speaking the strong Schur property holds iff an appropriate condition concerning sequences with positive pairwise disjoint terms is satisfied.   相似文献   

3.
New features of the Banach function space , that is, the space of all ν-scalarly pth power integrable functions (with 1?p<∞ and ν any vector measure), are presented. The Fatou property plays an essential role and leads to a new representation theorem for a large class of abstract p-convex Banach lattices.  相似文献   

4.
We construct a separable dual Banach latticeE such that no non-trivial order interval of its dual is weakly compact. HenceE has the Radon-Nikodym property without being in some sense a dual in a natural way. The final draft of this paper was written while the author held a grant from NATO to visit the Ohio State University.  相似文献   

5.
6.
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   

7.
8.
LetE be a 1-injective Banach lattice,X any Banach space andT: E ← X a norm bounded linear operator. Then eitherT is an isomorphism on some copy ofl inE or for all σ > 0 there is φ ∈E + such that ‖Tu‖≦φ (|u|)+σ ‖u‖ for alluE. We deduce the theorem that: A norm order continuous injective Banach lattice is order isomorphic to an (AL)-space.  相似文献   

9.
10.
11.
12.
New features of the Banach function space L1w(v), that is, the space of all v-scalarly integrable functions (with v any vector measure), are exposed. The Fatou property plays an essential role and leads to a new representation theorem for a large class of abstract Banach lattices. Applications are also given to the optimal domain of kernel operators taking their values in a Banach function space.  相似文献   

13.
We study the geometry of plane domains and the uniform Hölder continuity properties of analytic functions.With 1 Figure  相似文献   

14.
15.
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 FBLC[E] containing a linear isometric copy of E and satisfying the following universal property: for every complex Banach lattice XC, every operator T:EXC admits a unique lattice homomorphic extension T?:FBLC[E]XC with 6T?6=6T6. The free complex Banach lattice FBLC[E] 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 FBLC[E] and FBLC[F] are lattice isometric. The spectral theory of induced lattice homomorphisms on FBLC[E] is also explored.  相似文献   

16.
Reflexivity in Banach lattices   总被引:1,自引:0,他引:1  
  相似文献   

17.
18.
19.
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   

20.
Let X be a Banach lattice, and let ${x\in X{\setminus}\{0\}}$ . We study the structure of the set Grad(x), of all supporting functionals of x. If X is a Dedekind σ-complete Banach lattice, there is an isometry from Grad(x) onto Grad(|x|); hence the elements x and |x| are smooth simultaneously. And if, additionally, X* is strictly monotone then Grad(|x|) consists of positive functionals. As a by-product of our results we obtain that an arbitrary Banach lattice X is strictly monotone whenever its dual X* is smooth.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号