ON A NORMAL FORM FOR NON-WEAKLY SEQUENTIALLY CONTINUOUS POLYNOMIALS ON BANACH SPACES

Let p be an m-homogeneous polynomial on a complex Banach space, and let (xn)n be a bounded sequence such that when evaluated in polynomials of degree less than m, it converges to zero, but p(xn) = 1. It is proved here that there exists a basic sequence (yk)k equivalent to a subsequence (xnk)k, for which p( k=1 akyk) = k=1