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Necessary and sufficient conditions for invertibility of operators in spaces of real interpolation
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2013 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 264, no 1, 207-245 p.Article in journal (Refereed) Published
Abstract [en]

Let A be a bounded linear operator from a couple (X-0, X-1) to a couple (Y-0, Y-1) such that the restrictions of A on the end spaces X-0 and X-1 have bounded inverses defined on Y-0 and Y-1, respectively. We are interested in the problem of how to determine if the restriction of A on the space (X-0, XI)(theta,q) has a bounded inverse defined on the space (Y-0, Y-1)(theta,q). In this paper, we show that a solution to this problem can be given in terms of indices of two subspaces of the kernel of the operator A on the space X-0 + X-1.

Place, publisher, year, edition, pages
Elsevier , 2013. Vol. 264, no 1, 207-245 p.
Keyword [en]
Real interpolation, Invertibility of operators
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:liu:diva-87240DOI: 10.1016/j.jfa.2012.10.007ISI: 000312115100008OAI: oai:DiVA.org:liu-87240DiVA: diva2:587249
Available from: 2013-01-14 Created: 2013-01-14 Last updated: 2017-12-06

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Asekritova, IrinaKruglyak, Natan

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