Alladi Ramakrishnan Hall

The BCL theorem and factorization of the right-shift semigroup

Kalyan B Sinha

JNCASR

The classical Berger-Coburn-Lebow (BCL) theorem gives a unique factorization of the discrete semigroup $\{M_z^n \times I | n>=0\}$ in vector-valued Hardy space $H^2_D(E)$ in terms of contractive holomorphic semigroups. Here we study the (continuou) 1-parameter version of this and get a similar factorization with the associated infinitesmal, holomorphic generators giving rise to operator-valued Mobius transformations $D \times E$.