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Factorization and reflexivity on Fock spaces

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Abstract

The framework of the paper is that of the full Fock space\(\mathcal{F}^2 (\mathcal{H}_n )\) and the Banach algebraF ∞ which can be viewed as non-commutative analogues of the Hardy spacesH 2 andH ∞ respectively.

An inner-outer factorization for any element in\(\mathcal{F}^2 (\mathcal{H}_n )\) as well as characterization of invertible elements inF ∞ are obtained. We also give a complete characterization of invariant subspaces for the left creation operatorsS 1 ,..., S n of\(\mathcal{F}^2 (\mathcal{H}_n )\). This enables us to show that every weakly (strongly) closed unital subalgebra of {φ(S 1 ,..., S n ) ∶ φ∈F ∞} is reflexive, extending in this way the classical result of Sarason [S]. Some properties of inner and outer functions and many examples are also considered.

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Authors and Affiliations

  1. Division of Mathematics, Computer Science and Statistics, The University of Texas at San Antonio, 78249, San Antonio, TX, USA

    Alvaro Arias

  2. Division of Mathematics, Computer Science and Statistics, The University of Texas at San Antonio, 78249, San Antonio, TX, USA

    Gelu Popescu

Authors
  1. Alvaro Arias
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  2. Gelu Popescu
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Additional information

The first author was supported in part by NSF DMS 93-21369 1991Mathematics Subject Classification. Primary 47D25, Secondary 32A35, 47A67.

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Arias, A., Popescu, G. Factorization and reflexivity on Fock spaces. Integr equ oper theory 23, 268–286 (1995). https://doi.org/10.1007/BF01198485

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  • DOI: https://doi.org/10.1007/BF01198485

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