Accepted 12 January 1996 In December 1983, a 53-year old Chinese woman presented with a one-year history of generalised pruritus. Various members of her family, extending over four generations, had autoimmunne thyroid disorders. On examination, she had bilateral xanthelasmata but no stigmata of chronic liver disease nor jaundice. Her liver was just palpable but she had neither splenomegaly nor ...

In this paper we consider Bernstein’s Lethargy Theorem (BLT) in the context of Fréchet spaces. Let X be an infinite-dimensional Fréchet space and let V = {Vn} be a nested sequence of subspaces of X such that Vn ⊆ Vn+1 for any n ∈ N and X = ⋃∞ n=1 Vn. Let en be a decreasing sequence of positive numbers tending to 0. Under an additional natural condition on sup{dist(x, Vn)}, we prove that there e...

We prove that, if (C[a, b], {An}) is an approximation scheme and (An) satisfies de La Vallée-Poussin Theorem, there are instances of continuous functions on [a, b], real analytic on (a, b], which are “poorly approximable” by the elements of {An}. This illustrates the thesis that the smoothness conditions guaranteeing that a function is “well approximable” must be “global”. The failure of smooth...