赋s范数的Orlicz序列空间的β性质

β Property in Orlicz Sequence Spaces Equipped with s-norm

赋s范数的Orlicz空间是Orlicz空间的推广,为研究赋s范数Orlicz空间的H性质和β性质,首先对s范数的一些基本性质进行讨论。然后,在此基础上,给出了赋s范数的Orlicz序列空间具有H性质判据是Φ∈δ_(2),并得到了赋s范数的Orlicz序列空间具有β性质的充要条件为空间自反即Φ∈δ_(2)∩δ_(2)。

Orlicz spaces equipped with s-norm is an extension of Orlicz spaces.In order to studing the H property and the propertyβin Orlicz space equipped with s-norm,some basic properties of the s-norm are discussed firstly.Then,based on this,Φ∈δ_(2) which is the criteria of H property of Orlicz sequence spaces equipped with s-norm were given.In this paper,we get that the Orlicz sequence space equipped with s-norm have property β if and only if the spaces is reflexive,that isΦ∈δ_(2)∩δ_(2).