## ABSOLUTE CONVERGENCE WITH SPEED AND MATRIX TRANSFORMS

## ABSOLUTE CONVERGENCE WITH SPEED AND MATRIX TRANSFORMS

*A. Aasma, P. N. Natarajan*

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## Abstract

We de ne the notion of absolute convergence with speed, where the speed is de ned by a monotonically increasing positive sequence . Also we present the notion of absolute -conservativity of a matrix, and the notion of improvement of -convergence by a matrix. Let X; Y be two sequence spaces de ned by speeds of convergence. In this paper, we give necessary and su cient conditions for a matrix A (with real or complex entries) to map X into Y , if X or Y is the set of absolutely -convergent sequences. We also present some examples of matrices being absolutely -conservative or improving the absolute -convergence, and consider these problems in the special cases if A is the Riesz matrix (R; pn) or the Zweier matrix Z1=2.

## Keywords

Matrix transforms, convergence and absolute convergence with speed, absolute -conservativity, improvement of -convergence.