Characterization and properties of extreme operators into C(Y)

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Let E be a real (or complex) Banach space, Y a compact Hausdorff space, and C(Y) the space of real (or complex) valued continuous functions on Y. If T is an extreme point in the unit ball of bounded linear operators from E into C(Y), then it is shown that T * maps (the natural imbedding in C(Y) * of)Y into the weak *-closure of ext S(E *), provided that Y is extremally disconnected, or E=C(X), where X is a dispersed compact Hausdorff space.

Original languageEnglish
Pages (from-to)174-183
Number of pages10
JournalIsrael Journal of Mathematics
Issue number2
StatePublished - Jun 1972


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