L_p +L_q and L_p ∩ L_q are not isomorphic for all 1 ≤ p, q ≤ ∞, p ≠ q

2018/04/10 by С. В. Асташкин, Astashkin, Sergey, Lech Maligranda +1
Mathematics · #46B42 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46E30 #Secondary 42B20

paper · pdf · doi:10.48550/arxiv.1804.03469

openalex publication_date 2018/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if 1 ≤ p, q ≤ ∞, then the spaces L_p +L_q and L_p ∩ L_q are isomorphic if and only if p = q. In particular, L₂ +L_∞ and L₂ ∩ L_∞ are not isomorphic which is an answer to a question formulated in the paper S. V. Astashkin and L. Maligranda, \textitL_p + L_∞ and L_p ∩ L_∞ are not isomorphic for all 1 ≤ p < ∞, p ≠ 2, Proc. Amer. Math. Soc. 146 (2018), no. 5, 2181--2194.

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