Grothendieck's Theorem
Let 
and 
be paired spaces with 
a family of absolutely convex bounded sets of such that the sets of generate and, if 
, then there exists a 
such that 
and 
. Then 
is complete Iff algebraic linear functional 
of that is weakly continuous on every
is expressed as 
for some 
. When is not complete, the space of all linearfunctionals satisfying this condition gives the completion 
of .
References
Iyanaga, S. and Kawada, Y. (Eds.). ``Grothendieck's Theorem.'' §407L in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1274, 1980.
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