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关于一般化莫茨金序列空间,它们的矩阵转换和紧运算符的研究

Jun-Jie Quan¹, Devia Narrania², Kuldip Raj²

¹Department of Mathematics and Digital Sciences, Chengyi College, Jimei University, Xiamen, Fujian, China.

|August 20, 2025

概括

研究人员构建了新的概括的q差异莫茨金序列空间,并探索了它们的拓性质,包括基础和双空间. 他们还在这些新的数学空间中描述了矩阵映射和紧运算符.

科学领域:

* 数学分析
* 序列空间
* 功能分析

背景情况:

* 序列空间的现有研究为探索新的通用空间提供了基础.
* q差异和q-Motzkin矩阵是已知的数学工具.
*理解拓性质对于分析序列空间至关重要.

研究的目的:

* 构建和定义新的概括式q差异莫茨金序列空间.
* 调查这些新定义的空间的拓特征.
* 为了确定基数和计算双空间 (α-, β-, γ-双).
* 描述这些空间中的矩阵映射和紧运算符.

主要方法:

* q-Motzkin矩阵与一般化q-差异矩阵的组合.
* 应用拓分析技术
* 基础的确定和双空间的计算.
*使用豪斯多夫测量非紧度的矩阵映射和紧运算符的表征.

主要成果:

*成功构建了一般化的q差异莫茨金序列空间.
* 确定特定空间的基础 ([公式:见文本]和[公式:见文本]).
* 为新空间计算α,β和γ双元.
定义空间之间的矩阵映射的特征.
在空间上使用Hausdorff非紧度度的紧运算符的表征.

结论:

* 该研究成功引入并分析了新的泛化q差异莫茨金序列空间.
*已经确定了这些空间的拓性质,基础和二元性.
*对矩阵映射和紧运算符的描述为这些空间的结构提供了宝贵的见解.

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