The generalized Banach sequence spaces and their dual spaces based on permutation symmetric gauge norms
The generalized Banach sequence spaces and their dual spaces based on permutation symmetric gauge norms
复制标题
DOI：
10.1080/03081087.2022.2094867
复制
发表时间：
2022-09
影响因子：
1.1
通讯作者：
Yann-Kunn Chen;Tiantian Fu;Yehui Zhang
中科院分区：
文献类型：
--
作者：
Yann-Kunn Chen;Tiantian Fu;Yehui Zhang
本文引入并研究了序列空间上的一类范数α，称为置换对称规范范数，它恰当地包含了的经典范数类。我们定义了广义序列空间，证明了广义序列空间是Banach空间，并利用在上的投影得到了的刻画。对于对偶性，经典序列空间()中的预期结果在这些新的设置下仍然有效，包括对偶空间的刻画和Hölder不等式的存在性。值得指出的是，广义序列空间不是自反空间，它不同于通常的序列空间。
In the present paper, we introduce and study a class of norms α on the sequence space , called permutation symmetric gauge norms, which properly contains the classical class of . For each , we define the generalized sequence space , which is proved to be a Banach space, and then we obtain a characterization of in terms of the projection onto . For the duality, the expected results in the classical sequence spaces ( ) are still valid in these new settings, including the characterization of dual space and the existence of Hölder's inequality. It is worthy pointing out that the generalized sequence space is not a reflexive space, which is different from the usual sequence spaces.