具有弱正规结构的 Orlicz空间(英文)

Orlicz Spaces with Weakly Normal Structure

W.Kirk给出了弱正规结构 ( WNS)的概念 ,并证明了弱正规结构 ( WNS)蕴涵弱不动点性质 ,B.Sims给出了具有 ( k)性质的巴拿赫空间 ,并证明了 ( k)性质蕴涵弱正规结构 ,陈述涛给出了伪 -k( pseudo-( k) )性质及弱各向一致凸 ( WURED)的概念 ,推广了 B.Sims的结果 ,并讨论了 Orlicz序列空间是弱各向一致凸的充要条件 .本文利用实变函数理论及赋范线性空间中有关知识 ,给出 Orlicz函数空间是弱各向一致凸的充分必要条件 .所得以的结论和证明方法与序列空间情形都有实质不同 .

W. Kirk introduced the concept (WNS) and proved (WNS)(FPP). B. Sims introduced property (k) and proved (k)(WNS). CHEN Shu\|tao introduced pseudo-(k) property and weakly uniformly rotund in every directoin (WURED), generalized B.Sims′ result and gave the criteria that Orlicz sequence spaces (l M,‖·‖ 0),(l M,‖·‖) are (WURED). By the knowledge of function theory and normed linear spaces, we obtain the criteria that Orlicz function spaces (L M,‖·‖ 0),(L M,‖·‖) are weakly uniformly rotund in every direc tion (weakly uniformly rotund in every direction (WURED) implies weakly normal structure (WNS) in Banach space).