Functional analysis
Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q
Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 661-665.

We prove that if 1p,q, then the spaces Lp+Lq and LpLq are isomorphic if and only if p=q. In particular, L2+L and L2L are not isomorphic, which is an answer to a question formulated in [2].

Nous prouvons que si 1p,q, alors les espaces Lp+Lq et LpLq sont isomorphes si et seulement si p=q. En particulier, L2+L et L2L ne sont pas isomorphes, ce qui est une réponse à une question formulée dans [2].

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DOI: 10.1016/j.crma.2018.04.019
Astashkin, Sergey V. 1; Maligranda, Lech 2

1 Department of Mathematics, Samara National Research University, Moskovskoye shosse 34, 443086, Samara, Russia
2 Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden
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Astashkin, Sergey V.; Maligranda, Lech. Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q. Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 661-665. doi : 10.1016/j.crma.2018.04.019. http://www.numdam.org/articles/10.1016/j.crma.2018.04.019/

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