Isometric equivalence of isometries on 𝐻^{𝑝}

Cima, Joseph; Wogen, Warren

doi:10.1090/proc/13106

Isometric equivalence of isometries on $H^p$
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by Joseph A. Cima and Warren R. Wogen

Proc. Amer. Math. Soc. 144 (2016), 4887-4898

DOI: https://doi.org/10.1090/proc/13106

Published electronically: April 27, 2016

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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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