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Isomorphic structure of Cesàro and Tandori spaces
Samara State Univ, Dept Math & Mech, , Samara, Russia.Samara State Aerosp Univ, Samara , Russia .
Poznan Univ Tech, Inst Math, Poznan, Poland.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0002-9584-4083
2019 (English)In: Canadian Journal of Mathematics - Journal Canadien de Mathematiques, ISSN 0008-414X, E-ISSN 1496-2479, Vol. 71, no 3, p. 501-532Article in journal (Refereed) Published
Abstract [en]

We investigate the isomorphic structure of the Cesàro spaces and their duals, the Tandori spaces. The main result states that the Cesàro function space Ces∞ and its sequence counterpart ces∞ are isomorphic. This is rather surprising since Ces∞ (like Talagrand’s example) has no natural lattice predual. We prove that ces∞ is not isomorphic to ℓ∞ nor is Ces∞ isomorphic to the Tandori space L1 with the norm ∥f∥L1 = ∥f∥L1, where f(t) = esssups≥tf(s). Our investigation also involves an examination of the Schur and Dunford–Pettis properties of Cesàro and Tandori spaces. In particular, using results of Bourgain we show that a wide class of Cesàro–Marcinkiewicz and Cesàro–Lorentz spaces have the latter property.

Place, publisher, year, edition, pages
Cambridge University Press, 2019. Vol. 71, no 3, p. 501-532
Keywords [en]
Cesàro and Tandori sequence spaces, Cesàro and Tandori function spaces, Cesàro operator, Banach ideal space, symmetric space, Schur property, Dunford–Pettis property, isomorphism
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-74679DOI: 10.4153/CJM-2017-055-8ISI: 000468458800001Scopus ID: 2-s2.0-85066078576OAI: oai:DiVA.org:ltu-74679DiVA, id: diva2:1326600
Note

Validerad;2019;Nivå 2;2019-06-18 (johcin)

Available from: 2019-06-18 Created: 2019-06-18 Last updated: 2019-06-18Bibliographically approved

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Astashkin, SergeyMaligranda, Lech

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