Characterizations and extensions of Lipschitz-\(\alpha\) operators (Q2508585)

The authors define and study the spaces \(L^{\alpha}(K,X)\) and \(l^{\alpha} (K,X)\) on a compact metric space \((K,d)\), called the big and little Lipschitz-\(\alpha \) space, respectively. They prove that a map \(F\) from a compact metric space \(K\) into a Banach space \(X\) over the scalar field \(F\) is a Lipschitz-\(\alpha \) operator if and only if for each \(\sigma \in X^{*}\), the map \(\sigma \circ F\) is a Lipschitz-\(\alpha \) function on \(K\). The results obtained are of great academic interest.