Abstract
Let X be a completely regular Hausdorff space and Cb(X) be the Banach space of all real-valued bounded continuous functions on X, endowed with the uniform norm. It is shown that every weakly compact operator T from Cb(X) to a quasicomplete locally convex Hausdorff space E can be uniquely decomposed as T=T1+T2+T3+T4, where Tk:Cb(X)→E(k=1,2,3,4) are weakly compact operators, and T1 is tight, T2 is purely τ-additive, T3 is purely σ-additive and T4 is purely finitely additive. Moreover, we derive a generalized Yosida–Hewitt decomposition for E-valued strongly bounded regular Baire measures.
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