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Lp + L and Lp n L are not Isomorphic for all 1 ≤ p < ∞, p ≠ 2
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: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 146, no 5, p. 2181-2194Article in journal (Refereed) Published
Abstract [en]

We prove the result stated in the title. It comes as a consequence of the fact that the space Lp n L∞, 1 = p < ∞, p ≠ 2, does not contain a complemented subspace isomorphic to Lp. In particular, as a subproduct, we show that Lp nL∞ contains a complemented subspace isomorphic to l2 if and only if p = 2.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2018. Vol. 146, no 5, p. 2181-2194
Keywords [en]
Symmetric spaces, isomorphic spaces, complemented subspaces
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-67826DOI: 10.1090/proc/13928ISI: 000425993100030Scopus ID: 2-s2.0-85046626311OAI: oai:DiVA.org:ltu-67826DiVA, id: diva2:1187264
Note

Validerad;2018;Nivå 2;2018-03-02 (rokbeg)

Available from: 2018-03-02 Created: 2018-03-02 Last updated: 2018-05-21Bibliographically approved

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