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Book Information

Author(s): 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

1.: B. Aupetit and J. Zemánek, Local behavior of the spectral radius in Banach algebras, J. London Math. Soc. 23 (1981), 171-178. MR 602249
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).
3.: F. F. Bonsall and J. Duncan, Complete normed algebras, Springer-Verlag, New York, 1973. MR 423029
4.: J. B. Conway and B. B. Morrel, Behaviour of the spectrum under small perturbations, Proc. Roy. Irish Acad. Sect. A. 81 (1981), 55-63. MR 635579
5.: H. G. Dales, Automatic continuity, a survey, Bull. London Math. Soc. 10(1978), 129-183. MR 500923
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.: V. I. Istrǎţescu, Introduction to linear operator theory, Dekker, 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.: G. J. Murphy, Continuity of the spectrum and spectral radius, Proc. Amer. Math. Soc. 82 (1981), 619-621. MR 614889
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.: A. M. Sinclair, Continuous semigroups in Banach algebras, London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge (to appear). 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.: J. Zemánek, Properties of the spectral radius in Banach algebras, Inst, of Math. Polish Acad, of Sci. Preprint 136, 1978; Proc. Spectral Theory Semester, Banach Center Publ. 8, PWN, Warsaw (to appear). MR 738318

Review Information:
Journal: Bull. Amer. Math. Soc. 7 (1982), 628-633.
DOI: 10.1090/S0273-0979-1982-15074-1
PII: S 0273-0979(1982)15074-1

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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