The motivation is simple, as it's it is trivially right when p=2. $p=2$. When considering the duality between L^p(l^p) $L^p$ ($l^p$) and L^q(l^q) $L^q$ ($l^q$) when p $p$ and q $q$ are conjugate in the sense that 1/p+1/q=1, $1/p+1/q=1$, I wonder if L^p $L^p$ and l^p $l^p$ are the same in the sense of isometry. I tried to use the situation when p=2, $p=2$, however I find it difficult to give a linear homeomorphism.
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Does there exists exist an isometry between L^p $L^p$ and l^p?$l^p$? |
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Does there exists an isometry between L^p and l^p?The motivation is simple, as it's trivially right when p=2. When considering the duality between L^p(l^p) and L^q(l^q) when p and q are conjugate in the sense that 1/p+1/q=1, I wonder if L^p and l^p are the same in the sense of isometry. I tried to use the situation when p=2, however I find it difficult to give a linear homeomorphism.
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