Nonlinear functionals on C([0,1] × [0,1])

John Robert Baxter and Rafael Van Severen Chacon

Vol. 48 (1973), No. 2, 347–353

DOI: 10.2140/pjm.1973.48.347

Abstract

Let M be a compact Hausdorff space. Let 𝒞(M) denote the Banach space of continuous functions f on M. We are interested in functionals Φ on 𝒞(M) with the following properties: (i) |Φ(f)|≦∥f∥ for every f ∈𝒞(M), (ii) Φ(f + g) = Φ(f) + Φ(g) whenever fg = 0, (iii) Φ(f + α) = Φ(f) + α for every f ∈𝒞(M) and every real number α.

Mathematical Subject Classification 2000

Primary: 46E15

Milestones

Received: 5 July 1972

Revised: 20 October 1972

Published: 1 October 1973