If a matrix .4 transforms a sequence {z„} into the sequence {z, A is said to be regular. The well known necessary and sufficient conditions for A to be regular are1 (a) X^-i |g»,*| Wo, (b) limn^oo an,k = 0 for every fixed fe, (c) XXi a»j»«A»—»1 as w-»°o. It is known2 that if a regular matrix s...