摘要
利用Ｔａｐｉａ半内积（ｘ，ｙ）Ｔ＝ｌｉｍｔ→０＋［（ｘ＋ｔｙ２－ｘ２）／（２ｔ）］，ｘ，ｙ∈Ｘ，研究了Ｂａｎａｃｈ空间Ｘ的自反和逼近性质，并在光滑的Ｂａｎａｃｈ空间Ｘ上利用由Ｔａｐｉａ半内积定义的一类连续线性泛函Ｔ（Ｘ）＝｛ｆｘ∈Ｘ＊｜〈ｆｘ，ｙ〉＝（ｘ，ｙ）Ｔ；ｘ，ｙ∈Ｘ｝研究了Ｂａｎａｃｈ空间的严格凸、一致凸以及具有性质（Ｈ）的特征．
The reflexity and the approximation property in Banach space X are studied by use of T semi inner product (x,y) T= lim t→0 +[(‖x+ty‖ 2-‖x‖ 2)/(2t)],x,y∈X and a class of continuous linear functionals T(X)={f x∈X *|〈f x,y〉=(x,y) T ;x,y∈X} is defined. Using T semi inner product on smooth Banach Space X , the strict convexity, the uniform convexity, and the characterization with (H) property of Banach spaces are studied.
出处
《华中理工大学学报》
CSCD
北大核心
1998年第9期110-112,共3页
Journal of Huazhong University of Science and Technology
