Let A be a closed symmetric operator with deficiency indices n_+ and n_-. Then,

(a) A is self-adjoint if and only if n_+ = n_ = 0.

n_+ (A) = dim[ L_+] and n_- (A) = dim [L_-]

What is this saying? From that, how do I approach this problem?

Thanks for your help,

it is invaluable.