Contractively embedded invariant subspaces

Abstract

This paper focuses on representations of contractively embedded invariant subspaces in several variables. We present a version of the de Branges theorem for $n$-tuples of multiplication operators by the coordinate functions on analytic reproducing kernel Hilbert spaces over the unit ball ${\mathbb{B}}^n$ and the Hardy space over the unit polydics ${\mathbb{D}}^n$ in ${\mathbb{C}}^n$.

14 pages. To appear in Operator Theory Advances and Applications (Special volume honoring Joe Ball)