On polynomials that are weakly uniformly continuous on the unit ball of a Banach space

Abstract

We prove quantitative strengthenings of results on polynomials that are weakly uniformly continuous on the unit ball of a Banach space due to Aron, Lindstrom, Ruess, and Ryan (Proc. Amer. Math. Soc., 1999, 127, 1119-1125) and to Toma (Aplicacoes holomorfas e polinomios� -continuos. 1993). Our method is based on the uniform factorization of compact sets of compact operators.