If $H$ is a separable infinite-dimensional Hilbert space, then we can find a unitary isomorphism $H\cong\bigoplus_{n\in\mathbb{N}}H_n$ where each $H_n$ is an infinite-dimensional Hilbert space. If instead of $H$, I have $\ell_p$ ($1<p<\infty$), then what is the/an analogous (isometric) isomorphism statement? Should I be taking an $\ell_p$ direct sum of a countable collection of $\ell_p$'s?
2026-04-04 10:39:26.1775299166
$\ell_p$ direct sum of $\ell_p$'s
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