Shapiro's Theorem for subspaces

2010/09/28 by J. M. Almira, Almira, J. M., T. Oikhberg +1
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1009.5535

35 pages, submitted to a Journal

arxiv created 2011/08/26 · arxiv updated 2011/08/30

Abstract

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 ∈ An} ‖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.

Citations

• Approximation schemes satisfying Shapiro's Theorem

Cited by

• Approximation schemes satisfying Shapiro's Theorem
• A lethargy result for real analytic functions

Related

• On Shapiro's lethargy theorem and some applications
• Approximation schemes satisfying Shapiro's Theorem
• On the bounded approximation property on subspaces of ℓ_p when 0
• An example of an asymptotically Hilbertian space which fails the approximation property
• The Dual Form of the Approximation Property for a Banach Space and a Subspace