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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

References

1. Amir, D., Continuous function spaces with the separable projection property, Bull. Res. Counc. of Israel, 10F (1962), 163–164.Google Scholar
2. Amir, D., Projections onto continuous function spaces, Proc. Amer. Math. Soc. 15 (1964), 396–402.Google Scholar
3. Baker, J. W., Some uncomplemented subspaces of C(X) of the type C(X), Studia Math. 86 (1970), 85–103.Google Scholar
4. Baker, J. W., Uncomplemented C(X)-subalgebras of C(X), Trans. Amer. Math. Soc. 186 (1973), 1–15.Google Scholar
5. Baker, J. W. and R. C. Lâcher, Some mappings whose induced subalgebras are uncomplemented, to appear, Pacific J. Math.Google Scholar
6. C∞k, H., Continua which admit only the identity mapping onto non-degenerate subcontinua, Fund. Math. 60 (1967), 241–249.Google Scholar
7. Ditor, S. Z., On a lemma of Milutin concerning averaging operators in continuous function spaces, Trans. Amer. Math. Soc. 149 (1970), 443–452.Google Scholar
8. Ditor, S. Z., Averaging operators in C(S) and lower semicontinuous sections of continuous maps, Trans. Amer. Math. Soc. 175 (1973), 195–208.Google Scholar
9. Kuratowski, K., Topology I (New York, 1966).Google Scholar
10. Mazurkiewicz, S. and Sierpinski, W., Contributions à la topologie des ensembles dênombrables, Fund. Math. 1 (1920), 17–27.Google Scholar
11. Michael, E., Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 151–182.Google Scholar
12. Peîczyriski, A., Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions, Dissertationes Math. 58 (1968).Google Scholar
13. Peîczyriski, A., On C(S)-subspaces of separable Banach spaces, Studia Math. 31 (1968), 513–522.Google Scholar
14. Pelczyiiski, A. and Semadeni, Z., Spaces of continuous functions, III; Spaces Cip) for Q, without perfect subsets, Studia Math. 18 (1959), 211–222.Google Scholar
15. Semadeni, Z., Banach spaces of continuous functions, Vol. 1 (Warsaw 1971).Google Scholar