On isometric stability of complemented subspaces of ${L_p}$

Details On isometric stability of complemented subspaces of ${L_p}$ On isometric stability of complemented subspaces of ${L_p}$

1997-09-11

arxiv.org/abs/math/9709214v1

Mathematics

Functional Analysis

Scientific paper

We show that Rudin-Plotkin isometry extension theorem in $L_p$ implies that when $X$ and $Y$ are isometric subspaces of $L_p$ and $p$ is not an even integer, $1 \leq p < \infty$, then $X$ is complemented in $L_p$ if and only if $Y$ is; moreover the constants of complementation of $X$ and $Y$ are equal. We provide examples demonstrating that this fact fails when $p$ is an even integer larger than 2.

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