Abstract
In this paper, we study the isometric extension problem between the unit spheres of L ∞ ( Γ ) -type space and a Banach space E. We prove that every surjective isometry between the unit spheres S ( L ∞ ( Γ ) ) and S ( E ) can be extended to be a linear isometry of L ∞ ( Γ ) onto E. Moreover, we study this problem between C ( Ω ) and a Banach space and also get an affirmative answer.
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