Integral Equations and Operator Theory

, Volume 23, Issue 3, pp 268–286

Factorization and reflexivity on Fock spaces

  • Alvaro Arias
  • Gelu Popescu
Article

DOI: 10.1007/BF01198485

Cite this article as:
Arias, A. & Popescu, G. Integr equ oper theory (1995) 23: 268. doi:10.1007/BF01198485

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 spacesH2 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 operatorsS1,..., Sn of\(\mathcal{F}^2 (\mathcal{H}_n )\). This enables us to show that every weakly (strongly) closed unital subalgebra of {φ(S1,..., Sn) ∶ 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.

Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • Alvaro Arias
    • 1
  • Gelu Popescu
    • 2
  1. 1.Division of Mathematics, Computer Science and StatisticsThe University of Texas at San AntonioSan AntonioUSA
  2. 2.Division of Mathematics, Computer Science and StatisticsThe University of Texas at San AntonioSan AntonioUSA