International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 4, Pages 519-524
doi:10.1155/S0161171278000502
Research notes
Submatrices of summability matrices
Department of Mathematics, Kent State University, Kent 44242, Ohio, USA
Received 20 April 1978
Copyright © 1978 J. A. Fridy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
It is proved that a matrix that maps ℓ1 into ℓ1 can be obtained from any regular matrix by the deletion of rows. Similarly, a conservative matrix can be obtained by deletion of rows from a matrix that preserves boundedness. These techniques are also used to derive a simple sufficient condition for a matrix to sum an unbounded sequence.