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

Ronglu Li
  Department of Mathematics
  Harbin Institute of Technology
  Harbin 150001
Junming Wang
  Department of Mathematics
  Harbin University of Science and Technology
  Harbin 150080

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 $(\Omega, B(\Omega, X))$ consisting of a nonempty set $\Omega$ and $B(\Omega, X) = \{f\in X^{\Omega}:f(\Omega)$ is bounded$\}$, where $X$ is a locally convex space.
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