Shapiro's Theorem for subspaces

Details Shapiro's Theorem for subspaces Shapiro's Theorem for subspaces

2010-09-28

arxiv.org/abs/1009.5535v2

Mathematics

Classical Analysis and ODEs

35 pages, submitted to a Journal

Scientific paper

In a previous paper (see arXiv:1003.3411 [math.CA]), we investigated the existence of an element x of a quasi-Banach space X whose errors of best approximation by a given approximation scheme (A_n) (defined by E(x,A_n) = \inf_{a \in A_n} \|x - a_n\|) decay arbitrarily slowly. In this work, we consider the question of whether x witnessing the slowness rate of approximation can be selected in a prescribed subspace of X. In many particular cases, the answer turns out to be positive.

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