A New Systems Theory Perspective on Canonical Wiener-Hopf Factorization on the Unit Circle

Abstract We establish left and right canonical factorizations of Hilbert-space operator-valued functions G ( z ) that are analytic on neighborhoods of the complex unit circle $${\mathbb {T}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> and the origin 0 and that have the form $$G(z)=I+F(z)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo