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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Vydáno v:	Journal of approximation theory s. 106213
Hlavní autoři:	Asekritova, Irina, Kruglyak, Natan, Mastyło, Mieczysław
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Inc 01.08.2025
Témata:	Fredholm operator Interpolation method Invertible operator Invertible operator Fredholm operator Interpolation method primary
ISSN:	0021-9045
On-line přístup:	Získat plný text
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Popis
Shrnutí:	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