Weak thresholding greedy algorithms in Banach spaces

abstract

• We consider weak thresholding greedy algorithms with respect to Markushevich bases in general Banach spaces. We find sufficient conditions for the equivalence of boundedness and convergence of the approximants. We also show that if there is a weak thresholding algorithm for the system which gives the best n-term approximation up to a multiplicative constant, then the system is already "greedy". Similar results are proved for "almost greedy" and "semi-greedy" systems. 2012 Elsevier Inc.

authors

• Schlumprecht, Thomas

published proceedings

• Journal of Functional Analysis

author list (cited authors)

• Dilworth, S. J., Kutzarova, D., Schlumprecht, T. h., & Wojtaszczyk, P.

citation count

• 3

complete list of authors

• Dilworth, SJ||Kutzarova, Denka||Schlumprecht, Th||Wojtaszczyk, P

publication date

• January 2012

publisher

• Elsevier  Publisher

published in

• Journal of Functional Analysis  Journal

Digital Object Identifier (DOI)

• 10.1016/j.jfa.2012.09.011

start page

• 3900

end page

• 3921

volume

• 263

issue

• 12

URL

• http://dx.doi.org/10.1016/j.jfa.2012.09.011