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<inf>p</inf> into l<inf>q</inf> where 1 ≤ p, q < ∞. Sağır and Güngör defined the superposition operator P<inf>g</inf> by P<inf>g</inf>(x) = (g(k, s, x<inf>ks</inf>))∞<inf>k,s=1</inf> for all real double sequences (x<inf>ks</inf>) where g: N2 × R → R and gave continuity of the superposition operator acting from the double sequence spaces L<inf>p</inf> into L<inf>q</inf> for 1 ≤ p, q < ∞. 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<inf>ks</inf>) and q = (q<inf>ks</inf>) are bounded double sequences of positive numbers. © Shiraz University 2017.