Article ID Journal Published Year Pages File Type
4591861 Journal of Functional Analysis 2008 14 Pages PDF
Abstract

We give a new proof that every linear fractional map of the unit ball induces a bounded composition operator on the standard scale of Hilbert function spaces on the ball, and obtain new norm bounds analogous to the standard one-variable estimates. We also show that Cowen's one-variable spectral radius formula extends to these operators. The key observation underlying these results is that every linear fractional map of the ball belongs to the Schur–Agler class.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory