Invertible and Fredholm operators on interpolation scales

We investigate the behaviour of invertible and Fredholm operators on interpolation scales constructed via a family of interpolation functors {Fθ}θ∈(0,1). This family includes both complex and real interpolation functors. Our results demonstrate, in particular, that kernels and cokernels of operators...

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Bibliographic Details
Published in:Journal of approximation theory p. 106213
Main Authors: Asekritova, Irina, Kruglyak, Natan, Mastyło, Mieczysław
Format: Journal Article
Language:English
Published: Elsevier Inc 01.08.2025
Subjects:
Fredholm operator
Interpolation method
Invertible operator
Invertible operator
Fredholm operator
Interpolation method
primary
ISSN:0021-9045
Online Access:Get full text
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Summary:We investigate the behaviour of invertible and Fredholm operators on interpolation scales constructed via a family of interpolation functors {Fθ}θ∈(0,1). This family includes both complex and real interpolation functors. Our results demonstrate, in particular, that kernels and cokernels of operators are stable on intervals of parameters θ where the operators are Fredholm. Additionally, we introduce the notion of Fredholm operators in the category of Banach couples, establishing its relevance for the obtained results.
ISSN:0021-9045
DOI:10.1016/j.jat.2025.106213