Please help in Analysis function

**HallsofIvy** · January 8th 2013, 05:26 AM

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 $T^{-1}(p+ q)= T^{-1}(T(u)+ T(v))$ ?

**soso123** · January 9th 2013, 01:58 PM

Hi HallsofIvy, thanks for your answer

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

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