论文标题
扩展后的等效性和相对规则运算符的schur耦合
Equivalence after extension and Schur coupling for relatively regular operators
论文作者
论文摘要
最近在[24]中表明，扩展后的Banach太空运营商关系等效性（SC）并不能通过表征对基本无与伦比的Banach空间的操作员来表征这些关系来重合。证明非协调性的例子是弗雷德霍尔姆操作员，这是相对常规运营商的子类，后者是具有互补内核和范围的运营商。在本文中，我们分析了相对常规运营商类别的关系EAE和SC，导致了同等的Banach太空运营商问题，从中我们得出了新的案例，其中EAE和SC重合并为EAE和SC不合时宜，而Banach空间本质上是无与伦比的。
It was recently shown in [24] that the Banach space operator relations Equivalence After Extension (EAE) and Schur Coupling (SC) do not coincide by characterizing these relations for operators acting on essentially incomparable Banach spaces. The examples that prove the non-coincidence are Fredholm operators, which is a subclass of relatively regular operators, the latter being operators with complementable kernels and ranges. In this paper we analyse the relations EAE and SC for the class of relatively regular operators, leading to an equivalent Banach space operator problem from which we derive new cases where EAE and SC coincide and provide a new example for which EAE and SC do not coincide and where the Banach space are not essentially incomparable.
