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Joint spectra of commuting normal operators on Banach spaces

Published online by Cambridge University Press:  18 May 2009

Muneo Chō
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The joint spectrum for a commuting n-tuple in functional analysis has its origin in functional calculus which appeared in J. L. Taylor's epoch-making paper [19] in 1970. Since then, many papers have been published on commuting n-tuples of operators on Hilbert spaces (for example, [3], [4], [5], [8], [9], [10], [21], [22]).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 3 , September 1988 , pp. 339 - 345
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

1.Bonsall, F. F. and Duncan, J., Numerical ranges of operators on normed spaces and elements of normed algebras, (Cambridge Univ. Press, 1971).CrossRefGoogle Scholar
2.Bonsall, F. F. and Duncan, J., Numerical ranges II, (Cambridge Univ. Press, 1973).CrossRefGoogle Scholar
3.Ceausescu, Z. and Vasilescu, F.-H., Tensor product and the joint spectrum in Hilbert spaces, Proc. A.M.S. 72 (1978), 505–508.CrossRefGoogle Scholar
4.Ceausescu, Z. and Vasilescu, F.-H., Tensor product and Taylor's joint spectrum, Studia Math. 62 (1978), 305–311.CrossRefGoogle Scholar
5.Chō, M. and Takaguchi, M., Some classes of commuting n-tuple of operators, Studia Math. 80 (1984), 245–259.CrossRefGoogle Scholar
6.Chō, M., Joint spectra of operators on Banach spaces, Glasgow Math. J. 28 (1986), 69–72.CrossRefGoogle Scholar
7.Choi, M.-D. and Davis, C, The spectral mapping theorem for joint approximate point spectrum, Bull. A.M.S. 80 (1974), 317–321.CrossRefGoogle Scholar
8.Curto, R., On the connectedness of invertible n-tuples, Indiana Univ. Math. J. 29 (1980), 393–406.CrossRefGoogle Scholar
9.Curto, R., Fredholm and invertible n-tuples of operators, The deformation problem, Trans. A.M.S. 266 (1981), 129–159.Google Scholar
10.Curto, R., Spectral inclusion for doubly commuting subnormal n-tuples, Proc. A.M.S. 83 (1981), 730–734.Google Scholar
11.Dekker, N., Joint numerical ranges and joint spectrum of Hilbert space operators, (Ph.D. thesis, Amsterdam, 1969).Google Scholar
12.Harte, R., The spectral mapping theorem in several variables, Bull. A.M.S. 78 (1972), 871–875.CrossRefGoogle Scholar
13.Mattila, K., On proper boundary points of the spectrum and complemented eigenspaces, Math. Scand. 43 (1978), 363–368.CrossRefGoogle Scholar
14.Mattila, K., Normal operators and proper boundary points of the spectra of operators on Banach space, Ann. Acad. Sci. Fnn. A I, Math. Dissertations 19 (1978).Google Scholar
15.Mattila, K., Complex strict and uniform convexity and hyponormal operators, Math. Proc. Camb. Phil. Soc. 96 (1984), 483–493.CrossRefGoogle Scholar
16.McIntosh, A., Pryde, A. and Ricker, W., Comparison of joint spectra for certain classes of commuting operators, to appear.Google Scholar
17.McIntosh, A. and Pryde, A., A functional calculus for several commuting operators, submitted.Google Scholar
18.Slodkowski, Z. and Zelazko, W., On joint spectra of commuting families of operators, Studia Math. 50 (1974), 127–148.Google Scholar
19.Taylor, J. L., A joint spectrum for several commuting operators, J. Functional Anal. 6 (1970), 172–191.CrossRefGoogle Scholar
20.Taylor, J. L., The analytic functional calculus for several commuting operators, Acta Math. 125 (1970), 1–38.CrossRefGoogle Scholar
21.Vasilescu, F.-H., On pairs of commuting operators, Studia Math. 62 (1978), 203–207.CrossRefGoogle Scholar
22.Vasilescu, F.-H., A characterization of the joint spectrum in Hilbert spaces, Rev. Roum. Math. Pures Appl. 22 (1977), 1003–1009.Google Scholar
23.Wrobel, V., Joint spectra and joint numerical ranges for pairwise commuting operators in Banach spaces, Glasgow Math. J. 30 (1988), 145–153.CrossRefGoogle Scholar