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Book Review

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Book Information:

Author: Bernard Aupetit
Title: Propriétés spectrales des algèbres de Banach
Additional book information: Lecture Notes in Math., vol. 735, Springer-Verlag, Berlin and New York, 1979, xii + 192 pp., $13.80.

References [Enhancements On Off] (What's this?)

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  • 2. John Bachar et al, editors, Proceedings of the conference on automatic continuity and radical Banach algebras, Lecture Notes in Math., Springer-Verlag, Berlin and New York (to appear).
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  • 4. J. B. Conway and B. B. Morrel, Behaviour of the spectrum under small perturbations, Proc. Roy. Irish Acad. Sect. A 81 (1981), no. 1, 55–63. MR 635579
  • 5. H. G. Dales, Automatic continuity: a survey, Bull. London Math. Soc. 10 (1978), no. 2, 129–183. MR 500923, https://doi.org/10.1112/blms/10.2.129
  • 6. I. M. Gelfand, Normierte Ringe, Mat. Sb. 9 (1941), 3-21. (German, Russian summary) MR 4726
  • 7. S. Grabiner, The nilpotency of Banach nil algebras, Proc. Amer. Math. Soc. 21 (1969), 510. MR 236700
  • 8. R. Harte, The exponential spectrum in Banach algebras, Proc. Amer. Math. Soc. 58 (1976), 114-118. MR 407603
  • 9. Vasile I. Istrăţescu, Introduction to linear operator theory, Monographs and Textbooks in Pure and Applied Mathematics, vol. 65, Marcel Dekker, Inc., New York, 1981. MR 608969
  • 10. B. E. Johnson, The uniqueness of the (complete) norm topology, Bull. Amer. Math. Soc. 73 (1967), 407-409. MR 211260
  • 11. I. Kaplansky, Ring isomorphisms of Banach algebras, Canad. J. Math. 6 (1954), 374-381. MR 62960
  • 12. C. Le Page, Sur quelques conditions entraînant la commutativité dans les algèbres de Banach, C. R. Acad. Sci. Paris Sér. A-B 265 (1967), 235-237. MR 226409
  • 13. Gerard J. Murphy, Continuity of the spectrum and spectral radius, Proc. Amer. Math. Soc. 82 (1981), no. 4, 619–621. MR 614889, https://doi.org/10.1090/S0002-9939-1981-0614889-2
  • 14. J. D. Newburgh, The variation of spectra, Duke Math. J. 18 (1951), 165-176. MR 51441
  • 15. C. E. Rickart, General theory of Banach algebras, Van Nostrand, Princeton, N. J., 1960. MR 115101
  • 16. A. M. Sinclair, Automatic continuity of linear operators, London Math. Soc. Lecture Note Series, No. 21, Cambridge Univ. Press, Cambridge, New York, Melbourne, 1976. MR 487371
  • 17. Allan M. Sinclair, Continuous semigroups in Banach algebras, London Mathematical Society Lecture Note Series, vol. 63, Cambridge University Press, Cambridge-New York, 1982. MR 664431
  • 18. E. Vesentini, On the subharmonicity of the spectral radius, Boll. Un. Mat. Ital. 4 (1968), 427-429. MR 244766
  • 19. J. Zemánek, A note on the radical of a Banach algebra, Manuscripta Math. 20 (1977), 191-196. MR 435848
  • 20. Jaroslav Zemánek, Properties of the spectral radius in Banach algebras, Spectral theory (Warsaw, 1977) Banach Center Publ., vol. 8, PWN, Warsaw, 1982, pp. 579–595. MR 738318

Review Information:

Reviewer: Sandy Grabiner
Journal: Bull. Amer. Math. Soc. 7 (1982), 628-633
DOI: https://doi.org/10.1090/S0273-0979-1982-15074-1
American Mathematical Society