Banach空间ψ-直和的k严格凸性与Banach-Saks性质  

k Strict Convexity and Banach-Saks Property of ψ-direct Sums of Banach Spaces

作　　者：章志华[1] 王建[1] 

机构地区：[1]福建师范大学数学与计算机科学学院,福建福州350108

出　　处：《福建师范大学学报（自然科学版）》2010年第5期27-30,共4页Journal of Fujian Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10701063)

摘　　要：通过研究Banach空间ψ-直和的k严格凸性及Banach-Saks性质,证明了若X,Y分别是k严格凸与l严格凸的Banach空间,则XψY是k+l-1严格凸的(其中ψ∈Ψ是[0,1]上的严格凸函数),并将该结果推广到有限个Banach空间的ψ-直和.另外证明了XψY具BSP当且仅当X,Y具BSP.The k strict convexity and Banach-Saks property of ψ-direct sums of Banach spaces is studied,some results are gained.Let X,Y be Banach spaces.If X is k strict convex and Y is l strict convex,then XψY is k＋l-1 strict convex,where ψ∈Ψ is strict convex on.This result is generalized to finite ψ-direct sums of Banach spaces.In addition,XψY has Banach-Saks property if and only if X and Y have Banach-Saks property.

关 键 词：ψ-直和 k严格凸 巴拿赫空间 

分 类 号：O174.52[理学—数学]