Some complemented function spaces in C(X)

Daniel Eliot Wulbert

Vol. 24 (1968), No. 3, 589–602

DOI: 10.2140/pjm.1968.24.589

Abstract

et X and Z be compact Hausdorff spaces, and let P be a linear subspace of C(X) which is isometrically isomorphic to C(Z). In this paper conditions, some necessary and some sufficient, are presented which insure that P is complemented in C(X). For example if X is metrizable, P contains a strictly positive function, and the decomposition induced on X by P is lower semi-continuous then P is complemented in C(X).

Mathematical Subject Classification

Primary: 46.25

Milestones

Received: 16 August 1967

Published: 1 March 1968