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Cao, Huaixin; Zhang, Jianhua; Xu, Zongben

Characterizations and extensions of Lipschitz-\(\alpha\) operators. (English) Zbl 1111.47045

Acta Math. Sin., Engl. Ser. 22, No. 3, 671-678 (2006).
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.
Reviewer: Edward Prempeh (Kumasi)

Cited in 2 Reviews
Cited in 7 Documents

MSC:

47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems

Keywords:

uniform boundedness principle; extension theorems; Lipschitz-\(\alpha \) operator
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\textit{H. Cao} et al., Acta Math. Sin., Engl. Ser. 22, No. 3, 671--678 (2006; Zbl 1111.47045)
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References:

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