A de Branges-Beurling theorem for the full Fock space

2020/07/17 by Martin, Robert T. W., Shamovich, Eli
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2007.09145

Abstract

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

Related

• Sub-Hardy Hilbert spaces in the non-commutative unit row-ball
• Non-commutative rational Clark measures
• The Fock space as a de Branges-Rovnyak space
• Schur-class multipliers on the Fock space: de Branges-Rovnyak reproducing kernel spaces and transfer-function realizations
• Non-commutative rational functions in the full Fock space