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Hyponormal operators on uniformly smooth spaces

  • Muneo Chō (a1)

Abstract

In this paper we will characterize the spectrum of a hyponormal operator and the joint spectrum of a doubly commuting n-tuple of strongly hyponormal operators on a uniformly smooth space. We also describe some applications of these results.

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References

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[1]de Barra, G., ‘Some algebras of operators with closed convex numerical ranges’, Proc. Roy. Irish Acad. 72 (1972), 149154.
[2]de Barra, G., ‘Generalized limits and uniform convexity’, Proc. Roy. Irish Acad. 74 (1974), 7377.
[3]Beauzamy, B., Introduction to Banach spaces and their geometry, (North-Holland, 1985).
[4]Bonsall, F. F. and Duncan, J., Numerical ranges of operators on normed spaces and elements of normed algebras, (Cambridge Univ. Press, 1971).
[5]Bonsall, F. F. and Duncan, J., Numerical ranges II, (Cambridge Univ. Press, 1973).
[6]Chō, M., ‘Joint spectra of commuting normal operators on Banach spaces’, Glasgow Math. J. 30 (1988), 339345.
[7]Chō, M., ‘Hyponormal operators on uniformly convex spaces’, Acta Sci. Math. (Szeged), to appear.
[8]Chō, M., ‘Joint spectra of commuting pairs and uniform convexity’, Rev. Roumaine Math. Pures Appl. 34 (1989), 607614.
[9]Chō, M., ‘Semi-normal operators on uniformly smooth Banach spaces’, Glasgow Math. J. 42 (1990), 185192.
[10]Chō, M., ‘Joint spectra of strongly hyponormal operators on Banach spaces’, J. Math. Soc. Japan 42 (1990), 185192.
[11]Chō, M., ‘Weyl's theorem for hyponormal operators on Banach spaces’, J. Math. Anal. Appl., to appear.
[12]Choi, M.-D. and Davis, C., ‘The spectral mapping theorem for joint approximate point spectrum’, Bull. Amer. Math. Soc. 80 (1974), 317321.
[13]Curto, R., ‘On the connectedness of invertible n-tuples’, Indiana Math. J. 29 (1980), 393406.
[14]Harte, R., ‘The spectral mapping theorem in several variables’, Bull. Amer. Math. Soc. 78 (1972), 871875.
[15]Mattila, K., ‘Normal operators and proper boundary points of the spectra of operators on Banach space’, Ann. Acad. Sci. Fenn. Ser. A I D Math. Dissertationes 19 (1978).
[16]Mattila, K., ‘Complex strict and uniform convexity and hyponormal operators’, Math. Proc. Cambridge Philos. Soc. 96 (1986), 484493.
[17]McIntosh, A., Pryde, A. J. and Ricker, W., ‘Comparision of the joint spectra of certain classes of commuting operators’, Studia Math. 88 (1987), 2336.
[18]McIntosh, A., Pryde, A. J. and Ricker, W., ‘Systems of operator equations and pertubation of spectral subspaces of commuting operators’, Michigan Math. J. 35 (1988), 4364.
[19]Slodkowski, Z. and Zelazko, W., ‘On joint spectra of commuting families of operators’, Studia Math. 50 (1974), 127148.
[20]Taylor, J. L., ‘A joint spectrum for several commuting operators’, J. Funct. Anal. 6 (1970), 172191.
[21]Taylor, J. L., ‘The analytic functional calculus for several commuting operators’, Acta Math. 6 (1970), 138.
[22]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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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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