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- Jan 8th 2013, 01:07 AMsoso123Please help in Analysis function
- Jan 8th 2013, 05:26 AMHallsofIvyRe: Please help in Analysis function
For the first, use the ]Cauchy-Schwarz inequality, $\displaystyle ||x+y||\le ||x||+ ||y||$, and its consequence, $\displaystyle ||x- y||\ge ||x||- ||y||$.

The second looks straight forward. First, since T is 1-1 and onto, it**has**and inverse, a function $\displaystyle T^{-1}$, fro Y to X such that $\displaystyle T^{-1}(T(x))= x$ for all x in X and $\displaystyle T(T^{-1}(y))= y$ 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 $\displaystyle T^{-1}(p+ q)= T^{-1}(T(u)+ T(v))$? - Jan 9th 2013, 01:58 PMsoso123Re: Please help in Analysis function
Hi HallsofIvy, thanks for your answer

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