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Isometric equivalence of isometries on $ H^p$


Authors: Joseph A. Cima and Warren R. Wogen
Journal: Proc. Amer. Math. Soc. 144 (2016), 4887-4898
MSC (2010): Primary 47B32, 47B33, 30J05
DOI: https://doi.org/10.1090/proc/13106
Published electronically: April 27, 2016
MathSciNet review: 3544537
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Abstract: We consider a natural notion of equivalence for bounded linear operators on $ H^p,$ for $ 1 \leq p < \infty , p \neq 2.$ We study the structure of isometries on $ H^p$ of finite codimension and we determine when two such isometries are equivalent. Among these isometries, we determine which operators $ S$ satisfy $ \bigcap _1^{\infty } S^n H^p=(0).$


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Additional Information

Joseph A. Cima
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250
Email: cima@email.unc.edu

Warren R. Wogen
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599-3250
Email: wrw@email.unc.edu

DOI: https://doi.org/10.1090/proc/13106
Keywords: Hardy spaces, isometries
Received by editor(s): April 29, 2015
Received by editor(s) in revised form: September 8, 2015, January 13, 2016, and January 19, 2016
Published electronically: April 27, 2016
Communicated by: Pamela Gorkin
Article copyright: © Copyright 2016 American Mathematical Society

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