Unformatted text preview: X , and let f ( m ) be a linear functional deﬁned on M that satisﬁes 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 deﬁne 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 HahnBanach theorem, draw a diagram to illustrate it for the special case of a zerodimensional 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, nonnegative, and ﬁnite. 1...
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 Fall '09
 Math, Vector Space, normed vector space, Topological vector space, Luenberger, zerodimensional linear variety

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