The concept of absolute convergence for series is generalized to locally convex spaces and an invariant theorem for absolutely convergent series in duality is established: when a locally convex space
is weakly sequentially complete, an admissible topology which is strictly stronger than the weak topology on
in the dual pair (
) is given such that it has the same absolutely convergent series as the weak topology in
and Swartz, C.
Matrix Methods in Analysis
, Lecture Notes in Math., 1113, Springer-Verlag, 1985.
and Rogers, C. A.
, Absolute and unconditional convergence in normed linear spaces,
Proc. Nat. Acad. Sci., U.S.A.
Rogers C. A., 'Absolute and unconditional convergence in normed linear spaces' (1950) 36Proc. Nat. Acad. Sci., U.S.A.: 192-197.
Rogers C. A.Absolute and unconditional convergence in normed linear spacesProc. Nat. Acad. Sci., U.S.A.195036192197)| false