Frames and non linear approximations in Hilbert spaces

摘要

A simple proof of the proposition, stated in ([2], p. 346), asserting that in Hilbert spaces a Riesz basis is greedy, is given. Also, greedy approximant for frames in Hilbert spaces is defined and it is shown that frames satisfy the quasi greedy and almost greedy conditions. Finally, we give the characterizations of approximation spaces A (s) (I), A (q) (s) (I) by means of weak-l (p) and Lorentz sequence spaces for frames.