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WorldCat.org

University of California, Berkeley Department of Mathematics

The main question considered is a problem of Kaplansky. Suppose (OMEGA) is a compact Hausdorff space and let C((OMEGA)) denote the Banach algebra of continous complex valued functions with domain (OMEGA). The norm is the usual supnorm; for f in C((OMEGA)), (VBAR)(VBAR)f(VBAR)(VBAR) = sup (VBAR)f(x)(VBAR) (VBAR) x (ELEM) (OMEGA) . Assume (LAMDA) : C((OMEGA)) ( -->) B is a homomorphism of C((OMEGA)) into an arbitrary Banach algebra, B. Is (LAMDA) continuous?

Discontinuous homomorphisms of C(omega) and set theory