The orthogonal complement of $\mathcal{M}(a)$ in $\mathcal{H}(b)$
Volume 260 / 2021
Studia Mathematica 260 (2021), 327-340
MSC: Primary 47B32, 46E22; Secondary 30H10.
DOI: 10.4064/sm200918-5-1
Published online: 22 April 2021
Abstract
Let $b$ be a nonextreme function in the unit ball of $H^{\infty }$ on the unit disk $\mathbb D $ and let $a$ be an outer $H^{\infty }$ function such that $|a|^2+|b|^2=1$ almost everywhere on $\partial \mathbb D $. Sufficient and necessary conditions for the orthogonal complement of $\mathcal M (a)$ in $\mathcal H (b)$ to be finite-dimensional were given by D. Sarason (1994). Here we describe this space explicitly.
