对于所有$1 \leq p, q \leq \infty$、$p \neq q$，$L_p +L_q$和PDMATHAAB不是同构的
$L_p +L_q$ and $L_p \cap L_q$ are not isomorphic for all $1 \leq p, q \leq \infty$, $p \neq q$
摘要：
证明了如果$1 \leq p, q \leq \infty$，则空间$L_p +L_q$与空间$L_p \cap L_q$同构当且仅当$p = q$ .特别地，$L_2 +L_{\infty}$和$L_2 \cap L_{\infty}$不是同构的，这是对论文S中提出的问题的回答。V. Astashkin和L. Alberranda，\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.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
