A de Branges-Beurling theorem for the full Fock space
Autor: | Eli Shamovich, Robert T. W. Martin |
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Rok vydání: | 2021 |
Předmět: |
Power series
Pure mathematics Applied Mathematics 010102 general mathematics Mathematics - Operator Algebras Mathematics::Classical Analysis and ODEs Space form Hardy space 01 natural sciences Functional Analysis (math.FA) Fock space Mathematics - Functional Analysis 010101 applied mathematics Lattice (module) symbols.namesake Bounded function FOS: Mathematics Taylor series symbols Equivalence relation 0101 mathematics Operator Algebras (math.OA) Analysis Mathematics |
Zdroj: | Journal of Mathematical Analysis and Applications. 496:124765 |
ISSN: | 0022-247X |
DOI: | 10.1016/j.jmaa.2020.124765 |
Popis: | 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. |
Databáze: | OpenAIRE |
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