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.