Sequence transformations that guarantee a given rate of convergence
Gerd H. Fricke, John A. Fridy · Pacific Journal of Mathematics · 1990
Let t be a positive number sequence and define the sequence space Ω(ί) := {x: Xk = 0(4)}.Characterizations are given for matrices that map the spaces I 1 , l°° , c, or c 0 into Ω(/), thus ensuring that the transformed sequence converges at least as fast as t.These results yield information about matrices that map Z 1 , /°° , c, or c 0 into G := UΓG(O, l) Ω(r"), the set of geometrically dominated sequences.