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Unformatted text preview: X , and let f ( m ) be a linear functional dened on M that satises f ( m ) p ( m ) for all m M . Let y be a vector in X that is not in M . Prove that it is possible to dene a linear functional g on the subspace [ M + y ] such that g ( x ) p ( x ) for all x [ M + y ]. 8 State the geometric version of the Hahn-Banach theorem, draw a diagram to illustrate it for the special case of a zero-dimensional linear variety in R 2 , and prove it by using the extension form of the theorem. You may take it as proved that the Minkowski functional of a convex set is sublinear, continuous, non-negative, and nite. 1...
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This document was uploaded on 08/30/2011.
- Fall '09