On lower and upper bounds of matrices

Peng Gao

Published 2009-04-20, updated 2009-06-16Version 2

Using an approach of Bergh, we give an alternate proof of Bennett's result on lower bounds for non-negative matrices acting on non-increasing non-negative sequences in $l^p$ when $p \geq 1$ and its dual version, the upper bounds when $0<p \leq 1$. We also determine such bounds explicitly for some families of matrices.