Similarity of operators and geometry of eigenvector bundles

TL;DR

This paper characterizes contractions similar to the backward shift in Hardy space by examining the geometric structure of their eigenvector bundles, providing insights into operator similarity.

Contribution

It offers a new geometric criterion for operator similarity to the backward shift in Hardy space, linking eigenvector bundle geometry to operator theory.

Findings

Contractions similar to the backward shift are characterized by eigenvector bundle geometry.

Provides a geometric framework for understanding operator similarity.

Advances the understanding of operator classification in Hardy spaces.

Abstract

We characterize the contractions that are similar to the backward shift in the Hardy space $H^2$. This characterization is given in terms of the geometry of the eigenvector bundles of the operators.