Extending surjective isometries defined on the unit sphere of $\ell_\infty(\Gamma)$

Publication date: 27 September 2017

Abstract: Let

G a m m a

be an infinite set equipped with the discrete topology. We prove that the space

e l l_{i n f t y} (G a m m a),

of all complex-valued bounded functions on

G a m m a

, satisfies the Mazur-Ulam property, that is, every surjective isometry from the unit sphere of

e l l_{i n f t y} (G a m m a)

onto the unit sphere of an arbitrary complex Banach space

X

admits a unique extension to a surjective real linear isometry from

e l l_{i n f t y} (G a m m a)

to

X

.

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