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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Averaging operators in $ C(S)$ and lower semicontinuous sections of continuous maps


Author: Seymour Z. Ditor
Journal: Trans. Amer. Math. Soc. 175 (1973), 195-208
MSC: Primary 46E15; Secondary 46J10, 47B99
MathSciNet review: 0312228
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Abstract: For certain kinds of compact Hausdorff spaces S, necessary and sufficient topological conditions are provided for determining if there exists a norm 1 projection of $ C(S)$ onto any given separable selfadjoint subalgebra A, the conditions being in terms of the decomposition that A induces on S. In addition, for arbitrary S and selfadjoint closed subalgebra A of $ C(S)$, some results on lower bounds for the norms of projections of $ C(S)$ onto A are obtained. An example is given which shows that the greatest lower bound of the projection norms need not be attained.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0312228-8
PII: S 0002-9947(1973)0312228-8
Keywords: Averaging operator, regular averaging operator, projection operator, complemented subalgebra, continuous function space, Milutin space, lower semicontinuous section, lower bounds for norms of averaging operators
Article copyright: © Copyright 1973 American Mathematical Society