A rearrangement invariant space isometric to $L_p$ coincides with $L_p$

Details A rearrangement invariant space isometric to $L_p$ coincides with $L_p$ A rearrangement invariant space isometric to $L_p$ coincides with $L_p$

1995-09-10

arxiv.org/abs/math/9509213v1

Mathematics

Functional Analysis

Scientific paper

The following theorem is the main result of this note. Theorem 1. Let $(E,
\|\cdot\|_E) $ be a rearrangement invariant Banach function space on the
interval $[0, 1]$. If $E$ is isometric to $\L_p [0, 1]$ for some $1\le
p<\infty$, then $E$ coincides with $\L_p [0, 1]$ and furthermore $\|\cdot\|_E =
\lambda\|\cdot\|_{\L_p}$, where $\lambda = \|{\bf 1}\|_E$.

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