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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Norm reduction of averaging operators


Authors: H. B. Cohen, M. A. Labbe and J. Wolfe
Journal: Proc. Amer. Math. Soc. 35 (1972), 519-523
MSC: Primary 46E15
DOI: https://doi.org/10.1090/S0002-9939-1972-0324389-X
MathSciNet review: 0324389
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Abstract: Suppose $ \phi :S \to T$ is an irreducible map of compact Hausdorff spaces, and $ \mu :T \to M(S)$ the integral representation of an averaging operator for $ \phi $. We obtain an inequality of the form $ \left\Vert {\mu (t)} \right\Vert \leqq \left\Vert \mu \right\Vert - a(t)$, where $ a(t){\text{is}}$ a positive number depending on t. From this, some results of Amir and Isbell-Semadeni on $ {P_\lambda }$ spaces are shown to follow quickly and a theorem on the isomorphism of certain continuous function spaces is derived.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0324389-X
Keywords: $ {P_\lambda }$ spaces, averaging operator, Gleason map, regular Borel measure, extension operator, isomorphism
Article copyright: © Copyright 1972 American Mathematical Society