Hello everybody, I am new in the forum, nice to meet you, please help me with this problem.
Let such that: for all , i.e. is an isometry, for all . Show that , for all . Conclude that there is and a such that .
Thanks
Hello Drexel, thanks for your answer, here is my work
Using Cauchy’s inequality
.
By hypotesis, , then
(1)
Taking by
,
I get .
By the mean value theorem, there is a c in <0,1> such that
This latter using (1)
Hence
.
That's all, but i do not what else to do
Hugs
Hello Drexwl, thanks for your answer, here is my work
Using Cauchy’s inequality
.
By hypotesis, , then
(1)
Taking by
,
I get .
By the mean value theorem, there is a c in <0,1> such that
This latter using (1)
Hence
.
That's all, but i do not what else to do
Hugs