Weak and strong convergence of amarts in Fréchet spaces

Leo Egghe

Journal of Multivariate Analysis, 1982, vol. 12, issue 2, 291-305

Abstract: Several new characterizations of nuclearity in Fréchet spaces are proved. The most important one states tat a Fréchet space is nuclear if and only if every mean bounded amart is strongly a.s. convergent. This extends the result in [[2], 1798-1799] in a more positive way, and gives a different proof of it. The results of Brunel and Sucheston [C. R. Acad. Sci. Paris Ser. A (1976), 1011-1014], are extended to yield the same characterization of reflexivity of a Fréchet space in terms of weak convergence a.s. of weak amarts.

Date: 1982
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