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本文对几类B值小指标鞅空间建立了原子分解定理,利用原子分解讨论了它们之间的相互嵌入关系,其原子分解的存在性和它们之间的关系均与Banach空间的凸性和光滑性有密切联系. 相似文献
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平削算子生成的B值鞅空间及其原子分解 总被引:3,自引:3,他引:0
对于一系列由平削算子生成的Banach空间值鞅空间建立了原子分解定理 ,并以此为工具讨论了它们之间的相互嵌入关系 ,其结果与Banach空间的凸性和光滑性有密切联系 . 相似文献
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Banach空间值鞅上的拟局部算子 总被引:1,自引:0,他引:1
本文研究了拟局部算子在几个Banach空间值鞅空间上的有界性.给出了几个有界性定理,证明了鞅空间的简单原子分解.得到几个极大算子和p均方算子的一系列鞅不等式以及鞅空间的包含关系. 相似文献
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引入了原子鞅与正则原子鞅概念、并研究了两类Banach空间值鞅Hardy空间的原子分解和有限鞅的稠密性,所得结论揭示了鞅Hardy空间正则原子鞅分解的存在性,有限鞅的稠密性和Banach空间的一致光滑性(或一致凸性)三者之间的内在联系. 相似文献
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本文证明了弱Hardy正规鞅空间wHp和wH^sp上的原子分解定理.利用鞅的原子分解给出了弱Hardy正规鞅空间上的次线性算子有界的一个充分条件.利用这个条件得到了关于正规鞅的一些弱Lp范数不等式和弱(p,p)型不等式.这些结果是经典Hp鞅论中一些重要结果的弱型对应. 相似文献
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本文研究了B值弱Hardy两指标鞅空间的原子分解理论,利用原子分解的方法, 获得了B值弱Hardy两指标鞅空间的相互嵌入关系,所得结果联系于Banach空间的几何性质. 相似文献
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X是Banach空间,对X的每一弱可分且弱紧的子集K,若(k,ω)可度量,则称X是次可分的。如果对任意的可分,则称X是拟可分的。本文证明了这两类新引入的空间比可分空间与弱紧生成的Banach空间都要广泛并且保留了可分空间的许多重要性质。 相似文献
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Lorentz序列空间的装球问题 总被引:1,自引:0,他引:1
Banach空间中装球问题的研究,近四十年来已取得了令人瞩目的发展。Banach空间的装球值的范围已经确定,L_p空间及Orlicz序列空间I_M等许多经典Banach空间装球值已经找到.本文研究又一类经典Banach空间──Lorentz序列空间的装球问题,给出了Lorentz序列空间的装球值。 相似文献
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In [4], Freese and Murphy introduce a new class of spaces, the V-spaces, which include Banach spaces, hyperbolic spaces, and other metric spaces. In this class of spaces they investigate conditions which are equivalent to strict convexity in Banach spaces, and extend some of the Banach space results to this new class of spaces. It is natural to ask if known characterizations of real inner product spaces among Banach spaces can also be extended to this larger class of spaces. In the present paper it will be shown that a metrization of an angle bisector property used in [3] to characterize real inner product spaces among Banach spaces also characterizes real inner product spaces among V-spaces, and among another class of spaces, the L-spaces, which include hyperbolic spaces and strictly convex Banach spaces. In the process it is shown that in a complete, convex, externally convex metric space M, if the foot of a point on a metric line is unique, then M satisfies the monotone property, thus answering a question raised in [4]. 相似文献
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Frame expansions in separable Banach spaces 总被引:2,自引:0,他引:2
Banach frames are defined by straightforward generalization of (Hilbert space) frames. We characterize Banach frames (and Xd-frames) in separable Banach spaces, and relate them to series expansions in Banach spaces. In particular, our results show that we can not expect Banach frames to share all the nice properties of frames in Hilbert spaces. 相似文献
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Ju Myung Kim 《Journal of Mathematical Analysis and Applications》2007,327(1):257-268
This paper is concerned with the space of all compact adjoint operators from dual spaces of Banach spaces into dual spaces of Banach spaces and approximation properties. For some topology on the space of all bounded linear operators from separable dual spaces of Banach spaces into dual spaces of Banach spaces, it is shown that if a bounded linear operator is approximated by a net of compact adjoint operators, then the operator can be approximated by a sequence of compact adjoint operators whose operator norms are less than or equal to the operator norm of the operator. Also we obtain applications of the theory and, in particular, apply the theory to approximation properties. 相似文献
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本文处理能在Banach空间中实现的线性连续时间系统.这里,输入、输出和状态空间都是无穷维Banach空间.我们证明:加权模式有Banach空间实现的充要条件是它强连续且为指数阶.对状态算子是解析半群的无穷小生成元的情况,得到了Banach空间实现的存在性定理.所有定理都是在时间域中给出的. 相似文献
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本文证明了:Banach空间上完全分配格代数间的导子都是自动连续的;进而证明了套代数的可加导子是内的,套代数间的代数同构是自动连续的、空间的 相似文献
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In this article, the generalized Roper-Suffridge extension operator in Banach spaces for locally biholomorphic mappings is introduced. It is proved that this operator preserves the starlikeness on some domains in Banach spaces but does not preserves convexity for some cases. Moreover, the growth theorem, covering theorem, and the radius of starlikeness are discussed. Some results of Roper and Suffridge, Gong and Liu, Graham et al in C^n are extended to Hilbert spaces or Banach spaces. 相似文献
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A Banach partial *-algebra is a locally convex partial *-algebra whose total space is a Banach space. A Banach partial *-algebra is said to be of type (B) if it possesses a generating family of multiplier spaces that are also Banach spaces. We describe the basic properties of such objects and display a number of examples, namely L p -like function spaces and spaces of operators on Hilbert scales. 相似文献
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Satit Saejung 《Journal of Mathematical Analysis and Applications》2007,330(1):597-604
In this paper, we present some sufficient conditions for the uniform normal structure of Banach spaces and their dual spaces. More precisely, many known conditions implying the uniform normal structure of Banach spaces are shown to imply uniform normal structure of their dual spaces as well. 相似文献