On the joint spectral radius. II
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- by Muneo Chō, Tadasi Huruya and Volker Wrobel PDF
- Proc. Amer. Math. Soc. 116 (1992), 987-989 Request permission
Abstract:
In this paper we show that if ${\mathbf {T}} = ({T_1}, \ldots ,{T_n})$ is a commuting $n$-tuple of operators on a Hilbert space such that $\sigma ({\mathbf {T}}) = \Pi _{i = 1}^n\sigma ({T_i})$, then the algebraic joint spectral radius is equal to the geometric one.References
- John W. Bunce, Models for $n$-tuples of noncommuting operators, J. Funct. Anal. 57 (1984), no. 1, 21–30. MR 744917, DOI 10.1016/0022-1236(84)90098-3
- M. Ch\B{o} and T. Huruya, On the joint spectral radius, Proc. Roy. Irish Acad. Sect. A 91 (1991), no. 1, 39–44. MR 1173155
- Muneo Ch\B{o} and Makoto Takaguchi, Some classes of commuting $n$-tuples of operators, Studia Math. 80 (1984), no. 3, 245–259. MR 783993, DOI 10.4064/sm-80-3-245-259 M. Chō and W. Żelazko, On geometric spectral radius of commuting $n$-tuples of operators, preprint.
- Volker Wrobel, Joint spectra and joint numerical ranges for pairwise commuting operators in Banach spaces, Glasgow Math. J. 30 (1988), no. 2, 145–153. MR 942985, DOI 10.1017/S0017089500007163
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 987-989
- MSC: Primary 47A13
- DOI: https://doi.org/10.1090/S0002-9939-1992-1097339-1
- MathSciNet review: 1097339