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Averaging Operators and C(X)-Spaces with the Separable Projection Property

Published online by Cambridge University Press:  20 November 2018

John Warren Baker  and
John Wolfe
John Warren Baker
Affiliation:
Kent State University, Kent, Ohio
John Wolfe
Affiliation:
Oklahoma State University, Stillwater, Oklahoma
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The Banach space of bounded continuous real or complexvalued functions on a topological space X is denoted C(X). An averaging operator for an onto continuous function ϕ : X → Y is a bounded linear projection of C(X) onto the subspace ﹛ƒ ∈ C(X) : f is constant on each set ϕ -1(y) for y ∈ Y﹜. The projection constant p(ϕ) for an onto continuous map ϕ is the lower bound for the norms of all averaging operators for ϕ ﹛p(ϕ) = ∞ if there is no averaging operator for ϕ).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 5 , 01 October 1976 , pp. 897 - 904
Copyright
Copyright © Canadian Mathematical Society 1976

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