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A distance between orbits that controls commutator estimates and invertibility of operators
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Florida Atlantic University, Boca Raton.
2004 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 182, no 1, p. 78-123Article in journal (Refereed) Published
Abstract [en]

A distance between orbit spaces generated by a single element is introduced and it is shown that if an operator is invertible in one orbit it is also invertible in nearby orbits, thus proving a version of Shneiberg's theorem for orbital methods. The same machinery is used to extend the celebrated Rochberg-Weiss commutator theorem to the setting of orbital methods. It is shown that these results apply to the real and complex methods of interpolation by proving that these methods can be suitably obtained as orbits of a single element.

Place, publisher, year, edition, pages
2004. Vol. 182, no 1, p. 78-123
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-8196DOI: 10.1016/S0001-8708(03)00074-4ISI: 000188060500003Scopus ID: 2-s2.0-1642519697Local ID: 6aa85010-aaf0-11db-aeba-000ea68e967bOAI: oai:DiVA.org:ltu-8196DiVA, id: diva2:981087
Note
Validerad; 2004; 20070123 (kani)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Kruglyak, Natan

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