Banach Spaces of Lipschitz Functions and Vector-Valued Lipschitz Functions
Banach Spaces of Lipschitz Functions and Vector-Valued Lipschitz Functions
Introduction.Given a metric space (S, d) and a Banach space Ā£, let LipĀ£ (S, d) denote the set of bounded functions/: S -> Ā£ such that ll/IU = sup {\\f(s)-f(t)||d~\s, t)\s,teS,s*t} is finite.For/eLipĀ£(S, </), let ||/||" = sup{||/(j)|| |jeS}and ||/||= max (I/I "Ā”/I,).It is routine to show that || ā¢ ā¦