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A relation T with domain and range in a Hilbert space is said to be accretive if the transformation $ (T − \lambda)/(T + \bar \lambda\ ) $ with domain and range in the Hilbert space is contractive for some, and hence every, complex number $\lambda$ in the right half–plane.

How does some $\lambda$ imply for all $\lambda$? De branges states this in his "proof" of RH (infact uses it quite extensively). Also can anyone suggest references for such operators.

A relation T with domain and range in a Hilbert space is said to be accretive if the transformation $ (T − \lambda)/(T + \bar \lambda\ ) $ with domain and range in the Hilbert space is contractive for some, and hence every, complex number $\lambda$ in the right half–plane.

How does some $\lambda$ imply for all $\lambda$? De Branges states this in his "proof" of RH (in fact uses it quite extensively). Also can anyone suggest references for such operators.

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.

A relation T with domain and range in a Hilbert space is said to be accretive if the transformation $ (T − \lambda)/(T + \bar \lambda\ ) $ with domain and range in the Hilbert space is contractive for some, and hence every, complex number $\lambda$ in the right half–plane.

How does some $\lambda$ imply for all $\lambda$? De branges states this in his "proof" of RH  (infact uses it quite extensively). Also can anyone suggest references for such operators.