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Extensions of certain compact operators on vector-valued continuous functions


Author: Surjit Singh Khurana
Journal: Proc. Amer. Math. Soc. 102 (1988), 268-270
MSC: Primary 47B38,; Secondary 28B05,46G10,47B05
DOI: https://doi.org/10.1090/S0002-9939-1988-0920984-7
MathSciNet review: 920984
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Abstract: For any compact Hausdorff spaces $ X,Y$ with $ \varphi :\;X \to Y$ a continuous onto mapping, $ E,F$, Hausdorff locally convex spaces with $ F$ complete, $ C(X,E)\;(C(Y,E))$ all $ E$-valued continuous functions on $ X(Y)$, and $ L:C(Y,E) \to F$ a $ \mathcal{T}$-compact continuous operator $ (\sigma (F,F') \leq \mathcal{T} \leq \tau (F,F'))$, it is proved there exists a $ \mathcal{T}$-compact continuous operator $ {L_0}:C(X,E) \to F$ such that $ {L_0}(f \circ \varphi ) = L(f)$ for every $ f \in C(Y,E)$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0920984-7
Keywords: Submeasures, exhaustive submeasures, regular group-valued Borel measures, compact operators
Article copyright: © Copyright 1988 American Mathematical Society

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