For the first, use the ]Cauchy-Schwarz inequality, , and its consequence, .
The second looks straight forward. First, since T is 1-1 and onto, it has and inverse, a function , fro Y to X such that for all x in X and 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 ?
Hi HallsofIvy, thanks for your answer
Can you please explain to me more the answer to the first question