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Stability of Fredholm properties on interpolation Banach spaces
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
Adam Mickiewicz Univ, Poland.
2020 (English)In: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 260, article id 105493Article in journal (Refereed) Published
Abstract [en]

The main aim of this paper is to prove novel results on stability of the semi-Fredholm property of operators on interpolation spaces generated by interpolation functors. The methods are based on some general ideas we develop in the paper. This allows us to extend some previous work in literature to the abstract setting. We show an application to interpolation methods introduced by Cwikel-Kalton-Milman-Rochberg which includes, as special cases, the real and complex methods up to equivalence of norms and also some other well known methods of interpolation. A by-product of these results get the stability of isomorphisms on Calderon products of Banach function lattices. We also study the important characteristics in operator Banach space theory, the so-called modules of injection and surjection, and we prove interpolation estimates of these modules of operators on scales of the Calderon complex interpolation spaces. (C) 2020 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2020. Vol. 260, article id 105493
Keywords [en]
Fredholm operator; Interpolation functor; Interpolation spaces
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-171392DOI: 10.1016/j.jat.2020.105493ISI: 000582321800004OAI: oai:DiVA.org:liu-171392DiVA, id: diva2:1501013
Note

Funding Agencies|National Science Centre of PolandNational Science Center, PolandNational Science Centre, Poland [2015/17/B/ST1/00064]

Available from: 2020-11-15 Created: 2020-11-15 Last updated: 2020-11-15

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