Isometries of some Banach spaces of analytic functions |
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Authors: | William Hornor James E Jamison |
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Institution: | (1) Department of Mathematics, University of Southern Mississippi, 39406 Hattiesburg, MS;(2) Department of Mathematics, University of Memphis, 38152 Memphis, TN |
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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. |
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Keywords: | 46B04 46E15 |
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