A de Branges-Beurling theorem for the full Fock space

We extend the de Branges-Beurling theorem characterizing shift-invariant spaces boundedly contained in Hardy space of square-summable power series to full Fock over Cd. Here, is identified as Non-commutative (NC) Space Taylor several non-commuting variables. then proceed study lattice operations on NC kernels and operator-valued multipliers between vector-valued spaces. In particular, we demonstrate that with common coefficient range form a bounded general modulo natural equivalence relation.