Isometries of Some Banach Spaces of Analytic Functions
Document Type
Article
Publication Date
12-1-2001
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
We characterize the surjective isometries of a class of analytic functions on the disk which include the Analytic Besov spaceB p and the Dirichlet spaceD p. In the case ofB p we are able to determine the form of all linear isometries on this space. The isometries for these spaces are finite rank perturbations of integral operators. This is in contrast with the classical results for the Hardy and Bergman spaces where the isometries are represented as weighted compositions induced by inner functions or automorphisms of the disk.
Publication Title
Integral Equations and Operator Theory
Volume
41
Issue
4
First Page
410
Last Page
425
Recommended Citation
Hornor, W. E.,
Jamison, J. E.
(2001). Isometries of Some Banach Spaces of Analytic Functions. Integral Equations and Operator Theory, 41(4), 410-425.
Available at: https://aquila.usm.edu/fac_pubs/3728