Spectral properties of commuting operations for 𝑛-tuples

Abstract

Let R \textbf {R} and S \mathbf { S} be commuting n n -tuples. We give some spectral and local spectral relations between R S \mathbf { RS} and S R \mathbf { SR} . In particular, we show that R S \mathbf { RS} has the single valued extension property or satisfies Bishop’s property ( β ) (\beta ) if and only if S R \mathbf { SR} has the corresponding property.