Let and be paired spaces with a family of absolutely convex bounded sets of such that the sets of generate and, if , there exists a such that and . Then the dual space of is equal to the union of the weak completions of , where and .
See also Grothendieck's Theorem
References
Iyanaga, S. and Kawada, Y. (Eds.). ``Mackey's Theorem.'' §407M in
Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1274, 1980.