MathSciNet review: 1567391
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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.

• Bernard Aupetit and Jaroslav Zemánek, Local behaviour of the spectral radius in Banach algebras, J. London Math. Soc. (2) 23 (1981), no. 1, 171–178. MR 602249, DOI https://doi.org/10.1112/jlms/s2-23.1.171
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).
• Frank F. Bonsall and John Duncan, Complete normed algebras, Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80. MR 0423029
• 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
• H. G. Dales, Automatic continuity: a survey, Bull. London Math. Soc. 10 (1978), no. 2, 129–183. MR 500923, DOI https://doi.org/10.1112/blms/10.2.129
• I. Gelfand, Normierte Ringe, Rec. Math. [Mat. Sbornik] N. S. 9 (51) (1941), 3–24 (German, with Russian summary). MR 0004726
• Sandy Grabiner, The nilpotency of Banach nil algebras, Proc. Amer. Math. Soc. 21 (1969), 510. MR 236700, DOI https://doi.org/10.1090/S0002-9939-1969-0236700-9
• Robin Harte, The exponential spectrum in Banach algebras, Proc. Amer. Math. Soc. 58 (1976), 114–118. MR 407603, DOI https://doi.org/10.1090/S0002-9939-1976-0407603-5
• 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
• B. E. Johnson, The uniqueness of the (complete) norm topology, Bull. Amer. Math. Soc. 73 (1967), 537–539. MR 211260, DOI https://doi.org/10.1090/S0002-9904-1967-11735-X
• Irving Kaplansky, Ring isomorphisms of Banach algebras, Canad. J. Math. 6 (1954), 374–381. MR 62960, DOI https://doi.org/10.4153/cjm-1954-036-5
• Claude Le Page, Sur quelques conditions entraînant la commutativité dans les algèbres de Banach, C. R. Acad. Sci. Paris Sér. A-B 265 (1967), A235–A237 (French). MR 226409
• Gerard J. Murphy, Continuity of the spectrum and spectral radius, Proc. Amer. Math. Soc. 82 (1981), no. 4, 619–621. MR 614889, DOI https://doi.org/10.1090/S0002-9939-1981-0614889-2
• J. D. Newburgh, The variation of spectra, Duke Math. J. 18 (1951), 165–176. MR 51441
• Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
• Allan M. Sinclair, Automatic continuity of linear operators, Cambridge University Press, Cambridge-New York-Melbourne, 1976. London Mathematical Society Lecture Note Series, No. 21. MR 0487371
• 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
• Edoardo Vesentini, On the subharmonicity of the spectral radius, Boll. Un. Mat. Ital. (4) 1 (1968), 427–429 (English, with Italian summary). MR 0244766
• Jaroslav Zemánek, A note on the radical of a Banach algebra, Manuscripta Math. 20 (1977), no. 2, 191–196. MR 435848, DOI https://doi.org/10.1007/BF01170725
• 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

1.

B. Aupetit and J. Zemánek, Local behavior of the spectral radius in Banach algebras, J. London Math. Soc. 23 (1981), 171-178. MR 0602249

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