赋广义Orlicz范数的Orlicz函数空间的k一致凸点
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摘要
利用Banach空间基本理论和广义Orlicz范数的特征,研究赋广义Orlicz范数的Orlicz函数空间的局部k一致凸性,得到了由右导函数为连续函数的N-函数所生成的赋广义Orlicz范数的Orlicz函数空间中k一致凸点的判别准则,并且获得该空间局部k一致凸的条件.
Using the fundamental theories of Banach spaces and the characteristics of the generalized Orlicz norm,locally k-uniform rotundity of the Orlicz function spaces endowed with the generalized Orlicz norm is discussed.For the Orlicz function spaces generated by aN-function whose derivative on the right is continuous and endowed with the generalized Orlicz norm,the criterion of k-uniform rotund points in these spaces is presented.And both sufficient and necessary conditions are obtained to make these spaces be locally k-uniform rotund.
Using the fundamental theories of Banach spaces and the characteristics of the generalized Orlicz norm,locally k-uniform rotundity of the Orlicz function spaces endowed with the generalized Orlicz norm is discussed.For the Orlicz function spaces generated by aN-function whose derivative on the right is continuous and endowed with the generalized Orlicz norm,the criterion of k-uniform rotund points in these spaces is presented.And both sufficient and necessary conditions are obtained to make these spaces be locally k-uniform rotund.
引文
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[8]NAN C X,WANG J H.On the Lk-UR and L-kR spaces[J].Math Proc Cambridge Philis Soc,1988,104(3):521-526.
[9]HE R Y.The dual properties of LK-UR and k-SS space[J].Southeast Asian Bulletin of Mathematics,2002,26(2):215-221.
[10]王廷辅,崔云安.Orlicz空间的K-UR点[J].黑龙江大学自然科学学报,1995,12(3):13-20.
[11]CHEN S T.Geometry of Orlicz spaces[M].Warszawa:Dissertations Math,1996.
[12]段丽芬,左明霞,王宏志.赋广义Orlicz范数的Orlicz函数空间的UR点和WUR点[J].中山大学学报(自然科学版),2014,53(2):29-32.
[13]姜镕泽,王俊明,刘复生.赋p-Amemiya范数Orlicz空间的k-端点和k-强端点(1≤p≤∞)[J].哈尔滨理工大学学报,2011,16(2):90-93.
[2]南朝勋,王建华.k-严格凸性与k-光滑性[J].数学年刊,1990,11A(3):321-324.
[3]冼军,黎永锦.若干k-凸性的等价条件[J].中山大学学报(自然科学版),2003,42(1):12-15.
[4]SIMSEK N,SAVAS E,KARAKAYA V.On geometrical properties of some Banach spaces[J].Applied Mathematics&Information Sciences,2013,7(1):295-300.
[5]陈利国,罗成,王君.局部凸空间的中点局部k-一致凸性与中点局部k-一致光滑性[J].中山大学学报(自然科学版),2013,52(2):52-56.
[6]SULLIVAN F.A generalization of uniform rotund Banach spaces[J].Canad J Math,1979,31:628-636.
[7]王建华,余健波.LK-UR空间的一些性质[J].安徽师大学报(自然科学版),1988(1):1-5.
[8]NAN C X,WANG J H.On the Lk-UR and L-kR spaces[J].Math Proc Cambridge Philis Soc,1988,104(3):521-526.
[9]HE R Y.The dual properties of LK-UR and k-SS space[J].Southeast Asian Bulletin of Mathematics,2002,26(2):215-221.
[10]王廷辅,崔云安.Orlicz空间的K-UR点[J].黑龙江大学自然科学学报,1995,12(3):13-20.
[11]CHEN S T.Geometry of Orlicz spaces[M].Warszawa:Dissertations Math,1996.
[12]段丽芬,左明霞,王宏志.赋广义Orlicz范数的Orlicz函数空间的UR点和WUR点[J].中山大学学报(自然科学版),2014,53(2):29-32.
[13]姜镕泽,王俊明,刘复生.赋p-Amemiya范数Orlicz空间的k-端点和k-强端点(1≤p≤∞)[J].哈尔滨理工大学学报,2011,16(2):90-93.