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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 tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.ORCID-id: 0000-0002-9584-4083
2019 (engelsk)Inngår i: Canadian Journal of Mathematics - Journal Canadien de Mathematiques, ISSN 0008-414X, E-ISSN 1496-2479, Vol. 71, nr 3, s. 501-532Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
Cambridge University Press, 2019. Vol. 71, nr 3, s. 501-532
Emneord [en]
Cesàro and Tandori sequence spaces, Cesàro and Tandori function spaces, Cesàro operator, Banach ideal space, symmetric space, Schur property, Dunford–Pettis property, isomorphism
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
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
Merknad

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

Tilgjengelig fra: 2019-06-18 Laget: 2019-06-18 Sist oppdatert: 2019-06-18bibliografisk kontrollert

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