Abstract
We prove that every surjective isometry between unit spheres of $L^\infty(\Sigma,\Omega, \mu)$ and a Banach space $F$ can be linearly and isometrically extended to the whole space, which means that if the unit sphere of a Banach space $F$ is isometric to the unit sphere of $L^\infty(\Sigma,\Omega, \mu)$, then $F$ is linearly isometric to $L^\infty(\Sigma,\Omega, \mu)$.
Citation
Dong-Ni Tan. "Extension of Isometries on Unit Sphere of $L^\infty$." Taiwanese J. Math. 15 (2) 819 - 827, 2011. https://doi.org/10.11650/twjm/1500406236
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