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Spectral properties of commuting operations for $ n$-tuples


Authors: C. Benhida and E. H. Zerouali
Journal: Proc. Amer. Math. Soc. 139 (2011), 4331-4342
MSC (2010): Primary 47B20
DOI: https://doi.org/10.1090/S0002-9939-2011-10875-X
Published electronically: April 11, 2011
MathSciNet review: 2823078
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Abstract: Let $ {\bf 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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Additional Information

C. Benhida
Affiliation: UFR de Mathématiques - CNRS-UMR 8524, Université de Lille 1, Bât M2, 59655 Villeuneuve cedex, France
Email: benhida@math.univ-lille1.fr

E. H. Zerouali
Affiliation: Faculté des Sciences de Rabat, Université Mohammed V, BP 1014, Rabat, Morocco
Email: zerouali@fsr.ac.ma

DOI: https://doi.org/10.1090/S0002-9939-2011-10875-X
Keywords: $n$-tuples, Taylor spectrum, joint spectra, $SVEP$, Bishop’s property $(\beta)$.
Received by editor(s): February 16, 2009
Received by editor(s) in revised form: January 31, 2010, and October 6, 2010
Published electronically: April 11, 2011
Communicated by: Marius Junge
Article copyright: © Copyright 2011 American Mathematical Society

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