A characterisation of $L_1$-preduals in terms of extending Lipschitz maps

Abstract: We characterise the Banach spaces

X

which are

L_{1}

-predual as those for which every Lipschitz compact mapping

f : N l o n g r i g h t a r r o w X

admits, for every

v a r e p s i l o n > 0

and every

M

containing

N

, a Lipschitz (compact) extension

F : M l o n g r i g h t a r r o w X

so that

V e r t F V e r t l e q (1 + v a r e p s i l o n) V e r t f V e r t

. Some consequences are derived about

L_{1}

-preduals and about Lipschitz-free spaces.

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