Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0324389
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46E15

Retrieve articles in all journals with MSC: 46E15

Additional Information

Keywords: $ {P_\lambda }$ spaces, averaging operator, Gleason map, regular Borel measure, extension operator, isomorphism
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society