$\lambda$ point and $\lambda$ property in generalized Orlicz spaces with Luxemburg norm
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摘要: 为了研究在更一般情形下的Orlicz空间的$\lambda$性质, 借鉴经典Orlicz空间中的方法并发展了广义情形下的新方法, 给出了赋Luxemburg范数的广义Orlicz空间单位球中的点是$\lambda$点的充分必要条件. 这些结果表明, 在某些广义Orlicz空间中, 并不是所有单位球中的点都是$\lambda$点, 这与在经典Orlicz空间中, 单位球中的点都是$\lambda$点的结果是不同的. 最后, 给出了具有$\lambda$性质和一致$\lambda$性质的赋Luxemburg范数广义Orlicz空间的充要条件.
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关键词:
- 广义Orlicz空间 /
- Luxemburg范数 /
- $\lambda$性质 /
- $\lambda$点 /
- 一致$\lambda$性质
Abstract: In this paper, we gave the sufficient and necessary conditions of $\lambda$ point in a generalized Orlicz function space equipped with the Luxemburg norm, by methods used in classical Orlicz spaces and new methods introduced especially for generalized ones. The results indicate the difference between points in the unit balls of classical and that of generalized Orlicz spaces: all of the classical spaces are $\lambda$ points, but some of the generalized spaces are not. Finally, we gave the criteria of the $\lambda$ property and the uniform $\lambda$ property of generalized spaces. -
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