We prove quantitative strengthenings of results on polynomials that are weakly uniformly continuous on the unit ball of a Banach space due to Aron, Lindström, Ruess, and Ryan (Proc. Amer. Math. Soc., 1999, 127, 1119–1125) and to Toma (Aplicações holomorfas e polinômios τ-contínuos. 1993). Our method is based on the uniform factorization of compact sets of compact operators.
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https://doi.org/10.1515/crll.1980.313.195
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https://doi.org/10.1090/S0002-9939-99-04619-5
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