Assa-aree Sama-ae

pp. 451 - 466

Abstract

Let X ∈ {E_r(p)V , F_r(p)}, in this research, necessary and sufficient conditions are given for superposition operator to act from X into the space l₁ . Moreover, necessary and sufficient conditions are obtained
for superposition operator acting from X into l₁ to be locally bounded, bounded, and continuous.
Suppose that P_f is a superposition operator which acts from X into l₁ , it is found that
1. P_f is locally bounded if and only if f satisfies the condition A(2 ^/ ) ,
2. if P_f is bounded then f satisfies the condition A(2 ^/ ) ,
3. P_f is continuous if and only if f satisfies the condition A(2) .