Weak and strong convergence of amarts in Fréchet spaces

Abstract

most important one states tat a Frtchet space is nuclear if and only if every mean bounded amart is strongly as. convergent. This extends the result in [A. Bellow, Proc. Nat. Acad. Sci. USA 73, No. 6 (1976), 179&1799] in a more positive way, and gives a different proof of it. The results of Brunei and Sucheston [C. R. Acad. Sci. Paris Ser. A (1976), loll-10141 , are extended to yield the same characterization of reflexivity of a Frtchet space in terms of weak convergence a.s. of weak amarts.