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Equivalence After Extension and Schur Coupling for Relatively Regular Operators
Integral Equations and Operator Theory ( IF 0.8 ) Pub Date : 2020-08-26 , DOI: 10.1007/s00020-020-02597-2
S. ter Horst , M. Messerschmidt , A. C. M. Ran

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.

中文翻译:

相对正则算子的扩展和 Schur 耦合后的等价

最近在 [24] 中表明,Banach 空间算子关系扩展后的等效性 (EAE) 和 Schur 耦合 (SC) 通过表征作用于本质上无法比较的 Banach 空间的算子的这些关系而不一致。证明非重合的例子是 Fredholm 算子,它是相对正则算子的子类,后者是具有可补核和范围的算子。在本文中,我们分析了相对规则算子类的 EAE 和 SC 的关系,导致了一个等效的 Banach 空间算子问题,从中我们推导出了 EAE 和 SC 重合的新情况,并提供了一个 EAE 和 SC 不重合的新例子并且 Banach 空间在本质上并不是不可比的。
更新日期:2020-08-26
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