I don't understand why the functions in your post are functions of two variables. You want to show that the operator is a bilinear form, not the functions .
You want to show that
1)
2)
3) for any .
Here's the question:
Part (a)
I think to show bilinearity, I must prove these two conditions (left linear form & right linear form):
Can anyone show me how we can prove this, so I can get started? Thanks.
Edit: and