International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 4, Pages 519-524
doi:10.1155/S0161171278000502

Submatrices of summability matrices

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.