Hey,
For I have the following dilation operator:
I want to show that:
1) D maps into
2) D is linear and bounded
My answers:
1)
Firstly:
So to show that D maps into we must have that:
Correct so far? If yes, how to continue?
2)
Would it be sufficient first to show that an operator is bounded if there exists a such that:
Then I would show that the mapping is linear if:
Appreciate the effort.