Banach空间中的kWB性质(英文)

On Property kWB in Banach Spaces

采用一个新的几何性质 ｋＷＢ，证明了具有该性质的 Ｂａｎａｃｈ空间 Ｘ具有弱Ｂａｎａｃｈ一Ｓａｋｓ性质，且具有该性质的Ｂａｎａｃｈ空间Ｘ的ｋＮＵＣ充分必要条件是自反且为ＵＫＫ，并给出了Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ序列空间是ｋＮＵＣ的等价条件．

In this paper, we introduce a new geometric property, namely kWB. We proved that a Banach space X with kWB has the weak Banach - Saks property. We aslo get that if a Banach spach X has property kWB then it is kNUC if and only if it is reflexive and it has UKK. The sufficient and necessity condition for that Musielak - Orlicz sequence spaces equipped with the Luxemburg norm which have kNUC are obtained.