A de Branges-Beurling theorem for the full Fock space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:496

Article

Martin, Robert T. W.¹  Shamovich, Eli² 

[1] Univ Manitoba, Winnipeg, MB, Canada

[2] Ben Gurion Univ Negev, Beer Sheva, Israel

关键词: Noncommutative analysis;    Full Fock space;   

DOI  :  10.1016/j.jmaa.2020.124765

来源: Elsevier

【 摘 要 】

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 Spaceof 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. (C) 2020 Elsevier Inc. All rights reserved.

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