The equivalence of two matrices as bounded linear operators on \(l^p\) (Q1611446)

Making use of a theorem of \textit{G. Bennett} [Q. J. Math., Oxf. II. Ser. 38, 401-425 (1987; Zbl 0649.26013)] on bounded operators on \(l^p\), \(1< p < \infty\), in recent years several results have been given on the equivalence of some methods of weighted arithmetic means. The authors use the aforementioned theorem of G. Bennett once again to give a set of sufficient conditions for the equivalence of two methods of weighted arithmetic means over the class \(l^p\), \(1< p < \infty\). It may be noted that in the given theorem of the paper, none of the hypotheses involve the parameter \(p\). Thus the restriction \(l^p\), \(1< p < \infty\) in the conclusion is not justified. (This may appear to be the case in some earlier publications as well referred to in the paper).