Year: 2020
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Research Foundation
Awards: G1267154015, G4240710119
OpenAlex ID: W4285719990