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Joint spectra of commuting normal operators on Banach spaces

  • Muneo Chō

Extract

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]).

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References

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1.Bonsall, F. F. and Duncan, J., Numerical ranges of operators on normed spaces and elements of normed algebras, (Cambridge Univ. Press, 1971).
2.Bonsall, F. F. and Duncan, J., Numerical ranges II, (Cambridge Univ. Press, 1973).
3.Ceausescu, Z. and Vasilescu, F.-H., Tensor product and the joint spectrum in Hilbert spaces, Proc. A.M.S. 72 (1978), 505508.
4.Ceausescu, Z. and Vasilescu, F.-H., Tensor product and Taylor's joint spectrum, Studia Math. 62 (1978), 305311.
5.Chō, M. and Takaguchi, M., Some classes of commuting n-tuple of operators, Studia Math. 80 (1984), 245259.
6.Chō, M., Joint spectra of operators on Banach spaces, Glasgow Math. J. 28 (1986), 6972.
7.Choi, M.-D. and Davis, C, The spectral mapping theorem for joint approximate point spectrum, Bull. A.M.S. 80 (1974), 317321.
8.Curto, R., On the connectedness of invertible n-tuples, Indiana Univ. Math. J. 29 (1980), 393406.
9.Curto, R., Fredholm and invertible n-tuples of operators, The deformation problem, Trans. A.M.S. 266 (1981), 129159.
10.Curto, R., Spectral inclusion for doubly commuting subnormal n-tuples, Proc. A.M.S. 83 (1981), 730734.
11.Dekker, N., Joint numerical ranges and joint spectrum of Hilbert space operators, (Ph.D. thesis, Amsterdam, 1969).
12.Harte, R., The spectral mapping theorem in several variables, Bull. A.M.S. 78 (1972), 871875.
13.Mattila, K., On proper boundary points of the spectrum and complemented eigenspaces, Math. Scand. 43 (1978), 363368.
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).
15.Mattila, K., Complex strict and uniform convexity and hyponormal operators, Math. Proc. Camb. Phil. Soc. 96 (1984), 483493.
16.McIntosh, A., Pryde, A. and Ricker, W., Comparison of joint spectra for certain classes of commuting operators, to appear.
17.McIntosh, A. and Pryde, A., A functional calculus for several commuting operators, submitted.
18.Slodkowski, Z. and Zelazko, W., On joint spectra of commuting families of operators, Studia Math. 50 (1974), 127148.
19.Taylor, J. L., A joint spectrum for several commuting operators, J. Functional Anal. 6 (1970), 172191.
20.Taylor, J. L., The analytic functional calculus for several commuting operators, Acta Math. 125 (1970), 138.
21.Vasilescu, F.-H., On pairs of commuting operators, Studia Math. 62 (1978), 203207.
22.Vasilescu, F.-H., A characterization of the joint spectrum in Hilbert spaces, Rev. Roum. Math. Pures Appl. 22 (1977), 10031009.
23.Wrobel, V., Joint spectra and joint numerical ranges for pairwise commuting operators in Banach spaces, Glasgow Math. J. 30 (1988), 145153.
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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