Equivalence after extension and Schur coupling for relatively regular operators

Autor:	ter Horst, S., Messerschmidt, M., Ran, A. C. M.
Rok vydání:	2020
Předmět:	Mathematics - Functional Analysis 47A62 47A53 47A08
Druh dokumentu:	Working Paper
Popis:	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. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2005.14563 Zobrazit plný text záznamu View this record from Arxiv