Hilbert C ~*-模的模弱Banach-Saks和模Schur性质
Module weak Banach-Saks and module Schur properties of Hilbert C*-modules
摘要：
继续研究的巴拿赫萨克斯和舒尔属性开始（参见。M. Frank，A. A. C* 代数和Hilbert C*-模的Pavlov，Banach-Saks性质（已提交），我们在模的背景下研究了类似的性质。作为一个环境服务于Hilbert C*-模类。研究了Hilbert C ~*-模上弱模拓扑的一些性质。定义并研究了经典弱Banach-Saks性质和经典Schur性质的自然模模拟。给出了Hilbert C ~*-模的一些有用的性质.特别地，建立了这些性质与可数生成Hilbert C*-模的自对偶性之间的相互关系.
英文摘要：
Continuing the research on the Banach-Saks and Schur properties started in (cf. M. Frank, A. A. Pavlov, Banach-Saks properties of C*-algebras and Hilbert C*-modules (submitted)) we investigate analogous properties in the module context. As an environment serves the class of Hilbert C*-modules. Some properties of weak module topologies on Hilbert C*-modules are described. Natural module analogues of the classical weak Banach-Saks and the classical Schur properties are defined and studied. A number of useful characterizations of properties of Hilbert C*-modules is obtained. In particular, some interrelations of these properties with the self-duality property of countably generated Hilbert C*-modules are established.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
