Geodesic
Averaging Operators and C(X)-Spaces with the Separable Projection Property
Canadian journal of mathematics, Tome 28 (1976) no. 5, pp. 897-904

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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). 
Baker, John Warren; Wolfe, John. Averaging Operators and C(X)-Spaces with the Separable Projection Property. Canadian journal of mathematics, Tome 28 (1976) no. 5, pp. 897-904. doi: 10.4153/CJM-1976-087-4
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