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Characterization and properties of extreme operators intoC(Y)

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Abstract

LetE be a real (or complex) Banach space,Y a compact Hausdorff space, andC(Y) the space of real (or complex) valued continuous functions onY. IfT is an extreme point in the unit ball of bounded linear operators fromE intoC(Y), then it is shown thatT * maps (the natural imbedding inC(Y) * of)Y into the weak *-closure of extS(E *), provided thatY is extremally disconnected, orE=C(X), whereX is a dispersed compact Hausdorff space.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tel Aviv University, Tel Aviv

    M. Sharir

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  1. M. Sharir
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Sharir, M. Characterization and properties of extreme operators intoC(Y) . Israel J. Math. 12, 174–183 (1972). https://doi.org/10.1007/BF02764661

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  • DOI: https://doi.org/10.1007/BF02764661

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