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Math Help - Please help in Analysis function

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    Please help in Analysis function

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    Re: Please help in Analysis function

    For the first, use the ]Cauchy-Schwarz inequality, ||x+y||\le ||x||+ ||y||, and its consequence, ||x- y||\ge ||x||- ||y||.

    The second looks straight forward. First, since T is 1-1 and onto, it has and inverse, a function T^{-1}, fro Y to X such that T^{-1}(T(x))= x for all x in X and T(T^{-1}(y))= y for all y in Y. Now, suppose u and v are in X and let p= T(u), q= T(v). What can you say about T^{-1}(p+ q)= T^{-1}(T(u)+ T(v))?
    Last edited by Plato; January 8th 2013 at 06:49 AM.
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    Re: Please help in Analysis function

    Hi HallsofIvy, thanks for your answer

    Can you please explain to me more the answer to the first question
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