Algebraic pairs of isometries

2009/04/20 by Jim Agler, Agler, Jim, John E. McCarthy +3 · 2 citations
Mathematics · #14H50 #47B20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.0904.3130

openalex publication_date 2009/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider pairs of commuting isometries that are annihilated by a polynomial. We show that the polynomial must be inner toral, which is a geometric condition on its zero set. We show that cyclic pairs of commuting isometries are nearly unitarily equivalent if they are annihilated by the same minimal polynomial.

Cited by

• Constrained dilation and Γ-contractions
• A classification of n-tuples of commuting shifts of finite multiplicity

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