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Homework Help: Verify that the Riesz vector is unique

  1. Dec 9, 2012 #1
    1. The problem statement, all variables and given/known data
    The Riesz representation theorem gives us that forall f in V* there exists a unique R_f in V such that f(x) = <x, R_f >. (<,> is my attempt to type inner product angle brackets) Verify that R_f is unique.

    2. Relevant equations

    If I knew the relevant equations I think I could get this done on my own

    3. The attempt at a solution

    No attempts at a solution because i dont even know where to begin.

    Usually when i prove uniqueness I start with the assumption that two solutions exist and then prove that they end up being the same solution... but i dont see how to work that angle here.

    Any help would be great
     
  2. jcsd
  3. Dec 9, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    You already have the correct approach. Assume there are two solutions. Write down the equations the two vectors in V would have to satisfy.
     
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