Sequence transformations that guarantee a given rate of convergence

Gerd H. Fricke and John Albert Fridy

Vol. 146 (1990), No. 2, 239–246

DOI: 10.2140/pjm.1990.146.239

Abstract

Let t be a positive number sequence and define the sequence space Ω(t) := {x : x_k = O(t_k)}. Characterizations are given for matrices that map the spaces l¹, l^∞, c, or c₀ into Ω(t), thus ensuring that the transformed sequence converges at least as fast as t. These results yield information about matrices that map l¹, l^∞, c, or c₀ into G := ⋃ _r∈(0,1)Ω(rⁿ), the set of geometrically dominated sequences.

Mathematical Subject Classification 2000

Primary: 40A05

Milestones

Received: 20 March 1989

Published: 1 December 1990