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

Jingming Zhu

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arXiv · 1709.00260

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

Jingming Zhu

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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 $X=S^1$, 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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Jingming Zhu. 2017-09-01. Strongly Unitary Equivalence and Approximately Unitary Equivalence of Normal Compact Operators over Topological Spaces. https://arxiv.org/abs/1709.00260

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