Backward shifts on Banach spaces C(X)

Abstract

J. R. Holub conjectured that the Banach space C(X) of real valued continuous functions does not admit a backward shift, if X is a compact Hausdorff space with an infinite connected component. Here the conjecture is settled by proving that for arbitrary infinite compact Hausdorff spaces X, C(X) does not admit a backward shift. © 1996 Academic Press, Inc.