I have recently started normal operations, but I face with problems in this regard. please guide me.
a: let $ T \in K ( H ) $ be normal, show that $T \geq 0 $ if only if all eigenvalues( Special value) of the operator is equal to zero..
b:let $ T \in K ( H ) $ be $ T \geq 0 $, prove that There is a positive and unique compact actuator $ A$ so that $ A^{2} = T. $