共查询到20条相似文献,搜索用时 71 毫秒
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该文讨论了单位圆盘上不同Bers型空间之间的加权复合算子的有界性、紧性和弱紧性, 给出了一些充分必要的判别条件, 特别地得到不同Bers型空间上加权复合算子的紧性与弱紧性的等价性. 这些推广了经典的复合算子与乘法算子的相关结论. 该文同时也给出了Bers型空间上复合算子的Fredholm性和闭值域问题的刻画, 完善了文献[6]中结论. 相似文献
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本文主要研究Banach空间中的算子非紧性测度.我们首先给出Hausdorff算子非紧性测度关于Hausdorff度量的一个刻画;接着给出l~p (1≤p ∞)中Hausdorff算子非紧性测度的计算公式;最后给出了几种常见的算子非紧性测度等价的相关证明. 相似文献
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《数学物理学报(A辑)》2016,(5)
该文研究了Bergman空间A_α~p(B_n)上加权复合算子差的紧性问题.给出了两个加权复合算子之差为紧算子的一些充分和必要判据.同时也给出了某个加权复合算子与有限个加权复合算子之和的差为紧算子的一个完全刻画. 相似文献
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给出了BMOA空间上复合算子紧性的一个简单的充分必要条件.利用所给出的结果可以得到BMOA空间上紧复合算子必是Bloch空间和Hardy空间上的紧复合算子.文中也给出了VMOA空间上的类似结果. 相似文献
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讨论了不同Dirichlet型空间的广义Cesaro算子TΨ:D_α~p→D_β~q,给出了0p1、1pα+1或pn+1+α时T_Ψ是有界算子或紧算子的充要条件.同时,也给出了p取其它值时T_Ψ是有界算子或紧算子的充分条件或必要条件. 相似文献
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本文研究了无穷维Hamilton算子的可逆性问题,进而,刻画了无穷维Hamilton算子的谱的分布,并运用内部的逆紧性描述了无穷维Hamilton算子的逆紧性.最后,给出了无穷维Hamilton算子的可逆性问题在Dirac算子的可逆性问题中的应用. 相似文献
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本文给出了Dirichlet空间上Toelpitz算子为紧算子的充要条件.并证明具有C 相似文献
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设1
ω~p上非紧Toeplitz算子Tμ的本性范数等于其到紧Toeplitz算子集合的距离.更进一步,本文给出了此距离可以用无限个紧Toeplitz算子刻画. 相似文献
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Julio Flores 《Journal of Mathematical Analysis and Applications》2008,343(2):743-751
It is shown that every positive strictly singular operator T on a Banach lattice satisfying certain conditions is AM-compact and has invariant subspaces. Moreover, every positive operator commuting with T has an invariant subspace. It is also proved that on such spaces the product of a disjointly strictly singular and a regular AM-compact operator is strictly singular. Finally, we prove that on these spaces the known invariant subspace results for compact-friendly operators can be extended to strictly singular-friendly operators. 相似文献
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Belmesnaoui Aqzzouz Redouane Nouira Larbi Zraoula 《Proceedings of the American Mathematical Society》2007,135(4):1151-1157
We study several properties about the problem of domination in the class of positive AM-compact operators, and we obtain some interesting consequences on positive compact operators. Also, we give a sufficient condition under which a Banach lattice is discrete.
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We study the compactness of the class of operators which are AM-compact and semi-compact on Banach lattices and as consequences,
we obtain some characterizations of order continuous norms.
相似文献
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Julio Flores 《Journal of Mathematical Analysis and Applications》2009,354(2):657-663
The notion of disjointly homogeneous Banach lattice is introduced. In these spaces every two disjoint sequences share equivalent subsequences. It is proved that on this class of Banach lattices the product of a regular AM-compact and a regular disjointly strictly singular operators is always a compact operator. 相似文献
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We establish necessary and sufficient conditions under which the linear span of positive AM-compact operators (in the sense
of Fremlin) from a Banach lattice E into a Banach lattice F is an order σ-complete vector lattice. 相似文献
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Belmesnaoui Aqzzouz Redouane Nouira 《Proceedings of the American Mathematical Society》2006,134(12):3515-3523
We give different necessary and sufficient conditions so that the space of AM-compact operators is an order ideal and we deduce some consequences. R´ESUME. Nous donnons différentes conditions nécessaires et suffisantes pour que l'espace des opérateurs AM-compacts soit un idéal d'ordre et nous déduisons quelques conséquences.
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We establish some new necessary and sufficient conditions under which each regular operator is AM-compact if and only if its
adjoint is AM-compact. Also, we give some consequences. 相似文献
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In this paper we introduce and study the class of AM-totally bounded operators. Also we introduce the notion of graph lattice norm to prove a domination result for this class of operators. In particular, we extend the main theorem of Aqzzouz et al. [8]. Further, we give new results concerning the power domination problem by a totally bounded operator.
相似文献19.
Measures of Non-compactness of Operators on Banach Lattices 总被引:1,自引:0,他引:1
[Indag. Math.(N.S.)
2(2) (1991), 149–158; Uspehi Mat. Nauk
27(1(163)) (1972), 81–146] used representation spaces to study measures of non-compactness and spectral radii of operators on Banach lattices. In this paper, we develop representation spaces based on the nonstandard hull construction (which is equivalent to the ultrapower construction). As a particular application, we present a simple proof and some extensions of the main result of [J. Funct. Anal. 78(1) (1988), 31–55] on the monotonicity of the measure of non-compactness and the spectral radius of AM-compact operators. We also use the representation spaces to characterize d-convergence and discuss the relationship between d-convergence and the measures of non-compactness. 相似文献
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We characterize Banach lattices on which each positive Dunford-Pettis operator is AM-compact and we give some consequences. 相似文献