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On a class of linear operators on lp and its Schur multipliers
Department of Mathematics and Informatics, Technical University of Civil Engineering Bucharest, Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2016 (English)In: Proceedings of the Romanian Academy. Series A Mathematics, Physics, Technical Sciences, Information Science, ISSN 1454-9069, Vol. 17, no 2, 101-108 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we consider the spaces , , of infinite matrices defined by the norm . We consider the Schur product of matrices and prove that is not closed under this product. Moreover, we prove that linear and bounded operators on are Schur multipliers on , a result which is not obvious, since is not a Schur algebra. Most of the results are sharp in the sense that they are given via necessary and sufficient conditions. ( ) p w B 1p   A 1 ( ) =1 =1 1 0 := sup p p p jk k B j k w x p xk A a x            ( ) p w B p ( ) p w B ( ) p w B

Place, publisher, year, edition, pages
2016. Vol. 17, no 2, 101-108 p.
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-15153Local ID: ea2c84cb-96bb-4cd4-b7ca-3ec1f8d91819OAI: oai:DiVA.org:ltu-15153DiVA: diva2:988126
Note
Validerad; 2016; Nivå 2; 20160510 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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Persson, Lars-Erik

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