Orlicz序列空间的(k)性质

Property(k) of Orlicz Sequence Spaces

(k)性质是Banach空间中一个重要的几何性质,它与弱不动点性质密切相关。利用Banach空间及Orlicz空间的几何理论,研究(k)性质在一类具体的Banach空间——Orlicz序列空间中的刻画问题。给出了赋Luxemburg范数和赋Orlicz范数的Orlicz序列空间具有(k)性质的判别准则。作为推论,得到了这类空间具有弱不动点性质的一个充分条件。

Property （Q） is an important geometric property in Banach spaces, and it is closely associated witlifixed point property. By the geometric theory of Banach spaces and Orlicz spaces, we investigated thecharacterization for property（Q） in a special class of Banach spaces-Orlicz sequence spaces. Criteria for property（Q） in Orlicz sequence spaces equipped witii botii the Luxemburg norm and the Orlicz norm are given. As acorollary,the sufficient condition that t!iis kind of spaces has weak fixed point property is obtained.