If the result has been shown for the operators which has a norm , let , . If take and if then and . We can find an unique such that i.e. . We take .
in the book functional analysis by reed, there is a lemma which says:
If is a bounded linear operator on a Hilbert Space, and . Then there is a unique s.t.
I have a question about the proof. The author argues:
"It is sufficient to consider the case where ."
Why is it sufficient to proof just this case?
I couldn't find the right argument.