Spectral properties of commuting operations for 𝑛-tuples

Benhida, C.; Zerouali, E.

doi:10.1090/S0002-9939-2011-10875-X

Spectral properties of commuting operations for $n$-tuples
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by C. Benhida and E. H. Zerouali

Proc. Amer. Math. Soc. 139 (2011), 4331-4342

DOI: https://doi.org/10.1090/S0002-9939-2011-10875-X

Published electronically: April 11, 2011

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Abstract:

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

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