Vol. 66, No. 2, 1976

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Lattice projections on continuous function spaces

Emily Mann Peck

Vol. 66 (1976), No. 2, 477–490

Suppose that X is a compact Hausdorff space and that F is a closed (linear) sublattice of C(X). We characterize those sublattices F that are the ranges of (linear) Iattice projections on C(X): there is a lattice projection of C(X) onto F if and only if there is a closed subset Y of X such that F is lattice isomorphic to C(Y ) under the restriction mapping f f|Y (f F). Examples are given to show that this theorem cannot be substantially improved without imposing additional conditions either on X or on the sublattice F. If X is a stonian space, then a closed sublattice F of C(X) is the range of a lattice projection exactly when it is the range of a positive projection.

Mathematical Subject Classification 2000
Primary: 46E05
Received: 10 March 1976
Published: 1 October 1976
Emily Mann Peck