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arXiv · 1804.03469

$L_p +L_q$ and $L_p \cap L_q$ are not isomorphic for all $1 \leq p, q \leq \infty$, $p \neq q$

Sergey Astashkin·Lech Maligranda
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Abstract

We prove that if $1 \leq p, q \leq \infty$, then the spaces $L_p +L_q$ and $L_p \cap L_q$ are isomorphic if and only if $p = q$. In particular, $L_2 +L_{\infty}$ and $L_2 \cap L_{\infty}$ are not isomorphic which is an answer to a question formulated in the paper S. V. Astashkin and L. Maligranda, \textit{$L_p + L_{\infty}$ and $L_p \cap L_{\infty}$ are not isomorphic for all $1 \leq p < \infty, p \neq 2$}, Proc. Amer. Math. Soc. 146 (2018), no. 5, 2181--2194.

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Sergey Astashkin, Lech Maligranda. 2018-04-10. $L_p +L_q$ and $L_p \cap L_q$ are not isomorphic for all $1 \leq p, q \leq \infty$, $p \neq q$. https://arxiv.org/abs/1804.03469

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