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

Ditor, Seymour Z.

doi:10.1090/S0002-9947-1973-0312228-8

Averaging operators in $C(S)$ and lower semicontinuous sections of continuous maps
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by Seymour Z. Ditor PDF

Trans. Amer. Math. Soc. 175 (1973), 195-208 Request permission

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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