A de Branges-Beurling theorem for the full Fock space

Robert T.W. Martin, Eli Shamovich

Research output: Contribution to journalArticlepeer-review

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 Cd. 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.

Original languageEnglish
Article number124765
JournalJournal of Mathematical Analysis and Applications
Volume496
Issue number2
DOIs
StatePublished - 15 Apr 2021

Keywords

  • Full Fock space
  • Noncommutative analysis

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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