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 linear functionals satisfying
this condition gives the completion 
of 
.
Grothendieck's Theorem
See also
Mackey's TheoremExplore with Wolfram|Alpha
References
Iyanaga, S. and Kawada, Y. (Eds.). "Grothendieck's Theorem." §407L in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1274, 1980.Referenced on Wolfram|Alpha
Grothendieck's TheoremCite this as:
Weisstein, Eric W. "Grothendieck's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GrothendiecksTheorem.html