Strongly Unitary Equivalence and Approximately Unitary Equivalence of Normal Compact Operators over Topological Spaces

2017/09/01 by Jingming Zhu, Zhu, Jingming
Decision Sciences · Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.1709.00260

openalex publication_date 2017/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A and B be compact operators over a topological space X and suppose that these operators are normal and have same distinct eigenvalues at each point. By obstruction theory, we establish a necessary and sufficient condition for A and B to be strongly unitarily equivalent. When X=S¹, we also give a sufficient condition for A and B to be approximately unitarily equivalent with some assumption on their eigenvalues.

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