A relation T with domain and range in a Hilbert space is said to be accretive if the transformation $ (T − λ)/(T + \bar λ\ ) $ with domain and range in the Hilbert space is contractive for some, and hence every, complex number λ in the right half–plane. How does some λ imply for all λ? De branges states this in his "proof" of RH(infact uses it quite extensively). Also can anyone suggest references for such operators.