Invariant Property Of C₀(X)-Evaluation Convergence Of Operator Series

Invariant range of λ(X)- evaluation convergence in abstract duality pair is discussed. By introducing the concept of uniform vanish subsets of the spaces Co(X) and describing operator series family Cβ0(X), cβ(X),lβ(X),we get an equivalent proposition about uniform vanish subsets.Thus, the largest range of c0(X)- evaluation convergence of operator series in abstract duality pair is obtained .