无穷维费弗曼-迈耶对偶中的相对弱紧凑性

IF 1.2 3区 数学 Q1 MATHEMATICS
Vasily Melnikov
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引用次数: 0

摘要

让 E 是一个巴拿赫空间,使得 E′具有 Radon-Nikodým 属性。这项工作的目的是将 E 值鞅哈代空间 H1(μ,E) 中的相对弱紧凑性与较弱拓扑学中的凸紧凑性准则联系起来,例如度量紧凑上的均匀收敛拓扑学。这些结果代表了 Diestel、Ruess 和 Schachermayer 关于 L1(μ,E) 中相对弱紧凑性的深层结果的动态版本。在反向情况下,我们得到了 H1(μ,E) 有界序列的卡德克-佩乌琴斯基二分法,它将子序列分解为相对弱紧凑部分、点弱凸收敛部分和在度量紧凑上均匀收敛于零的空部分。作为推论,我们研究了向量值孔洛斯定理的参数化版本,而无需假设H1(μ,E)有界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Relative weak compactness in infinite-dimensional Fefferman-Meyer duality
Let E be a Banach space such that E has the Radon-Nikodým property. The aim of this work is to connect relative weak compactness in the E-valued martingale Hardy space H1(μ,E) to a convex compactness criterion in a weaker topology, such as the topology of uniform convergence on compacts in measure. These results represent a dynamic version of the deep result of Diestel, Ruess, and Schachermayer on relative weak compactness in L1(μ,E). In the reflexive case, we obtain a Kadec-Pełczyński dichotomy for H1(μ,E)-bounded sequences, which decomposes a subsequence into a relatively weakly compact part, a pointwise weakly convexly convergent part, and a null part converging to zero uniformly on compacts in measure. As a corollary, we investigate a parameterized version of the vector-valued Komlós theorem without the assumption of H1(μ,E)-boundedness.
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来源期刊
CiteScore
2.50
自引率
7.70%
发文量
790
审稿时长
6 months
期刊介绍: The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.
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