2009/10/15 by J. M. Almira, Almira, J. M.
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA
paper · pdf · doi:10.48550/arxiv.0910.2826
This paper has been withdrawn by the author because a full revision of it, with new and powerful contents, has been made with the help of another author and now the paper has been transformed in another completely different one which is common work with T. Oikhberg
arxiv created 2010/03/17 · arxiv updated 2010/03/19
In this paper we characterize the approximation schemes that satisfy Shapiro's theorem and we use this result for several classical approximation processes. In particular, we study approximation of operators by finite rank operators and n-term approximation for several dictionaries and norms. Moreover, we compare our main theorem with a classical result by Yu. Brundyi and we show two examples of approximation schemes that do not satisfy Shapiro's theorem.