Invariant Property Of C(X),l～p(X)-Evaluation Convergence Of Operator Series

Invariant range of λ(X)- evaluation convergence in abstract duality pair is discussed. we obtained the following results:1 With the concept of uniformly forward subsets of the spaces c(X),essentially bounded subsets of the spaces l∞(X) and uniformly exhaustive subsets of the spaces l~p(X) and the description of operator series family of l_p~β(X),we get a equipollence proposition about uniformly forward,essentially bounded and uniformly exhaustive subsets.2 Using the obtained theorem,the largest range of c(X),l~p(X)(1 < p ≤ ∞) — evaluation convergence of operator series in abstract duality pair is obtained.