Relations between some basic results derived from two kinds of topologies for a random locally convex module
Relations between some basic results derived from two kinds of topologies for a random locally convex module
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随机局部凸模块的两种拓扑得出的一些基本结果之间的关系
DOI：
10.1016/j.jfa.2010.02.002
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发表时间：
2010-05
影响因子：
1.7
通讯作者：
郭铁信
中科院分区：
文献类型：
--
作者：
郭铁信
本文的目的是展示随机局部凸模的两种拓扑（即(ε,λ)-拓扑和较强的局部l0 -凸拓扑）的一些基本结果之间的关系。首先，我们给出了已知的l0 -线性函数的Hahn-Banach扩展定理及其连续变分的一个极其简单的证明。然后给出了[D]中的超平面分离定理之间的关系。李建军，李建军，局部l0 -凸模的分离和对偶性，J.函数。[j] .数学学报，2009 (6):396 - 396郭红霞，肖红霞，陈晓霞，随机局部凸模的一个基本严格分离定理，非线性，71(2009)3794-3804：在此过程中我们还得到了一个非常有用的事实，即具有可数连接性质的随机局部凸模在两种拓扑下必须具有相同的完备性。作为这一事实的应用，我们证明了(ε,λ)-拓扑下随机赋范模的随机共轭空间的大部分先前建立的主要结果在局部l0 -凸拓扑下仍然有效，从而极大地丰富了随机赋范模的金融应用。
The purpose of this paper is to exhibit the relations between some basic results derived from the two kinds of topologies (namely the (ε,λ)-topology and the stronger locally L0-convex topology) for a random locally convex module. First, we give an extremely simple proof of the known Hahn–Banach extension theorem for L0-linear functions as well as its continuous variant. Then we give the relations between the hyperplane separation theorems in [D. Filipović, M. Kupper, N. Vogelpoth, Separation and duality in locally L0-convex modules, J. Funct. Anal. 256 (2009) 3996–4029] and a basic strict separation theorem in [T.X. Guo, H.X. Xiao, X.X. Chen, A basic strict separation theorem in random locally convex modules, Nonlinear Anal. 71 (2009) 3794–3804]: in the process we also obtain a very useful fact that a random locally convex module with the countable concatenation property must have the same completeness under the two topologies. As applications of the fact, we prove that most of the previously established principal results of random conjugate spaces of random normed modules under the (ε,λ)-topology are still valid under the locally L0-convex topology, which considerably enriches financial applications of random normed modules.
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影响因子：
1.3
作者：
T. Guo
通讯作者：
T. Guo
DOI：
--
发表时间：
2001-06
期刊：
Acta Analysis Functionalis Applicata
影响因子：
--
作者：
T. Guo
通讯作者：
T. Guo
DOI：
10.1007/s11425-008-0047-6
发表时间：
2008-08
期刊：
Science in China Series A: Mathematics
影响因子：
--
作者：
T. Guo
通讯作者：
T. Guo
影响因子：
1.3
作者：
T. Guo;Shaowen Li
通讯作者：
T. Guo;Shaowen Li
影响因子：
64.8
作者：
F. Smithies
通讯作者：
F. Smithies