Isometric Equivalence of Isometries on $ H^p $

TL;DR

This paper investigates the equivalence of isometries on Hardy spaces $H^p$ for $p eq 2$, classifies finite codimension isometries, and examines their Crownover property.

Contribution

It introduces a natural notion of equivalence for bounded linear operators on $H^p$ and classifies finite codimension isometries and their Crownover property.

Findings

Characterization of isometries of finite codimension on $H^p$

Classification of isometries with the Crownover property

Identification of equivalence classes of these isometries

Abstract

We consider a natural notion of equivalence for bounded linear operators on $H^p,$ for $p\neq 2.$ We determine which isometries of finite codimension are equivalent. For these isometries , we classify those which have the Crownover property.