I'm confused, please help.

[limpid lily]

I don't know how to go about this. I know the orthonormal sequence is used though.

[hearty mason]

ill do what i can but this question is quite ambitious for me. linearity implies the mapping f(x+a) = f(x) + f(a) isomorphisms
im guessing the lambda is for eigenvalues. the idea of an operator implies ring theory but this requires knowledge of fields which I have trouble with.

From what i can tell en are the basis for the hilbert space so there is a eigenvalue for each function since the norm is equal to the eigenvalue.

This looks like real analysis

Update me with anything new, Im interested in this problem

[limpid lily]

This is what I did, I considered the norm of D which follows the orthonormality of the basis {Ek}.

knowing the sequence is bounded, theres a constant that exists such that:

I then bounded the series

I then related to the norm, knowing that:

I get this

I square rooted both sides

it shows that D is bounded and the norm is:

If you catch anything I messed up on, please tell me.

[limpid lily]

.solved