Boundary behavior in Hilbert spaces of vector-valued analytic functions
The author studies the boundary behavior of functions in Hilbert spaces of vector-valued analytic functions on the unit disc \(\mathbb D\). More specifically, the author gives operator-theoretic conditions on \(M_z\), where \(M_z\) denotes the operator of multiplication by the identity function on \(\mathbb D\), that imply that all functions in the space have non-tangential limits a.e., at least on some subset of the boundary. The main part of the article concerns the extension of a theorem by \textit{A.\,Aleman, S.\,Richter} and \textit{C.\,Sundberg} [Trans.\ Am.\ Math.\ Soc.\ 359, No.\,7, 3369--3407 (2007; Zbl 1126.47023)] to the case of vector-valued functions.
scientific article; zbMATH DE number 5167467
scientific article