Kernels of bounded operators on Banach spaces.

Banach 空间上有界算子的核。

• 批准号: 2346321
• 金额: --
• 依托单位: Lancaster University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2346321
• 关键词: Kernels; bounded; operators; Banach; spaces.

In a recent paper, Laustsen and White initiated the study of the following question: which closed subspaces of a Banach space X can be realized as the kernel of a bounded linear operator from X to itself? They showed that every separable, closed subspace can be realized as such a kernel, but they also gave an example of a closed subspace of a reflexive Banach space which is not a kernel in this way, thus solving an open problem concerning dual Banach algebras. The purpose of this project is to investigate the above question further, beginning with the classical non-separable sequence spaces l_p(A) and c_0(A) for an uncountable index set A.

在最近的一篇论文中，Laustsen和白色发起了以下问题的研究：封闭的子空间的Banach空间X可以实现为内核的有界线性算子从X本身？他们证明了每个可分离的闭子空间都可以实现为这样的核，但他们也给出了一个自反Banach空间的闭子空间的例子，该子空间不是这样的核，从而解决了有关对偶Banach代数的一个公开问题。本项目的目的是进一步研究上述问题，从不可数指标集A的经典不可分序列空间l_p（A）和c_0（A）开始。