J. Aust. Math. Soc.  76 (2004), 369-381
Invariants in abstract mapping pairs

 Ronglu Li   Department of Mathematics   Harbin Institute of Technology   Harbin 150001   China
 and
 Junming Wang   Department of Mathematics   Harbin University of Science and Technology   Harbin 150080   China  wjmszx97@sina.com

Abstract
In a topological vector space, duality invariant is a very important property, some famous theorems, such as the Mackey-Arens theorem, the Mackey theorem, the Mazur theorem and the Orlicz-Pettis theorem, all show some duality invariants. In this paper we would like to show an important improvement of the invariant results, which are related to sequential evaluation convergence of function series. Especially, a very general invariant result is established for an abstract mapping pair  consisting of a nonempty set and  is bounded, where is a locally convex space.