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 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.