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Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q
Department of Mathematics Samara National Research University, Moskovskoye shosse 34, 443086, Samara, Russia .
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0002-9584-4083
2018 (English)In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569Article in journal (Refereed) Epub ahead of print
Abstract [en]

We prove that if 1≤p,q≤∞1≤p,q≤∞, then the spaces Lp+LqLp+Lq and Lp∩LqLp∩Lq are isomorphic if and only if p=qp=q. In particular, L2+LL2+L∞ and L2∩LL2∩L∞ are not isomorphic, which is an answer to a question formulated in [2].

Abstract [fr]

Nous prouvons que si 1≤p,q≤∞1≤p,q≤∞, alors les espaces Lp+LqLp+Lq et Lp∩LqLp∩Lq sont isomorphes si et seulement si p=qp=q. En particulier, L2+LL2+L∞ et L2∩LL2∩L∞ ne sont pas isomorphes, ce qui est une réponse à une question formulée dans [2].

Place, publisher, year, edition, pages
Elsevier, 2018.
Keyword [en]
Symmetric spaces, isomorphic spaces, complemented subspaces
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-68570DOI: 10.1016/j.crma.2018.04.019OAI: oai:DiVA.org:ltu-68570DiVA, id: diva2:1202884
Note

Fransk titel: [Lp + Lq et Lp ∩ Lq ne sont pas isomorphes pour tout 1 ≤ p,q ≤ ∞, p ≠ q]

Available from: 2018-05-02 Created: 2018-05-02 Last updated: 2018-05-15

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