Continuity of Superposition Operators on the Double Sequence Spaces of Maddox L(p)

Abstract

Petranuarat and Kemprasit (Southeast Asian Bull Math 21: 139-147, 1997) characterized continuity of the superposition operator acting from the sequence space l(p) into l(q) where 1 <= p, q < infinity. Sagir and Gungor defined the superposition operator P-g by P-g(x) = (g(k, s, x(ks)))(k,s= 1)(infinity) for all real double sequences (x(ks)) where g : N-2 x R -> R and gave continuity of the superposition operator acting from the double sequence spaces L-p into L-q for 1 <= p, q < infinity. In this paper, we characterize the continuity of the superposition operator acting from Maddox double sequence spaces L(p) into L(q)where p = (p(ks)) and q = (q(ks)) are bounded double sequences of positive numbers.