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Strict convexity of Orlicz sequence spaces equipped with p-Amemiya norms
Indian Journal of Pure and Applied Mathematics ( IF 0.7 ) Pub Date : 2021-07-27 , DOI: 10.1007/s13226-021-00157-x
Xiaoyan Li 1, 2 , Yunan Cui 1
Affiliation  

In this paper, criteria for strict convexity of Orlicz sequence spaces equipped with the p-Amemiya norms \((1\le p\le \infty )\) are presented. The obtained results widen the characterization of strict convexity of Orlicz sequence spaces. From our results it follows that there are Orlicz sequence spaces which are strictly convex for p-Amemiya norms with \(1<p<\infty \) only, that is, they are neither strictly convex for Luxemburg norm corresponding to the case \(p=\infty \) nor for Orlicz norm corresponding to the case \(p=1\).



中文翻译:

配备 p-Amemiya 范数的 Orlicz 序列空间的严格凸性

在本文中,提出了配备p -Amemiya 范数\((1\le p\le \infty )\)的 Orlicz 序列空间的严格凸性标准。所得结果拓宽了Orlicz序列空间严格凸性的刻画。从我们的结果可以看出,对于p -Amemiya 范数只有\(1<p<\infty \)存在 Orlicz 序列空间是严格凸的,也就是说,对于对应于情况\( p=\infty \)也不是对应于情况\(p=1\) 的Orlicz 范数。

更新日期:2021-07-27
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