Generalized Inner-Outer Factorization in non commutative Hardy Algebras

Abstract

Let $H^{\infty }(E)$ be a non commutative Hardy algebra, associated with a $W^{\ast }$-correspondence $E$. In this paper we construct factorizations of inner-outer type of the elements of $H^{\infty }(E)$ represented via the induced representation, and of the elements of its commutant. These factorizations generalize the classical inner-outer factorization of elements of $H^{\infty }(\mathbb{D})$. Our results also generalize some results that were obtained by several authors in some special cases.

arXiv admin note: text overlap with arXiv:1410.1788

References in corpus (1)

• Free Semigroupoid Algebras