Irina Asekritova, Natan Kruglyak, Mieczysław Mastyło, Invertible and fredholm operators in spaces of real interpolation, Vol. 2024 (2024), Article ID 25, pp. 1-18

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DOI: 10.23952/cot.2024.25

Received July 2, 2023; Accepted November 25, 2023; Published online April 2, 2024

 

Abstract. In this paper we suggest a new method for investigation of stability of Fredholm properties of operators on interpolation Banach spaces constructed by the real interpolation method. The method consists of two closely related steps. In the first step, invertible operators are investigated. In the second step, the results obtained for invertible operators are applied to investigation of Fredholm operators. This approach allows us to obtain results on stability of kernels and cokernels of Fredholm operators in the spaces constructed by the real interpolation method. A characterization of maximal intervals of parameter $\theta$ for which an operator T\colon \vec{X}_{\theta, q} \rightarrow \vec{Y}_{\theta, q} is Fredholm is also obtained.

 

How to Cite this Article:
I. Asekritova, N. Kruglyak, M. Mastyło, Invertible and fredholm operators in spaces of real interpolation, Commun. Optim. Theory 2024 (2024) 25.