Bulletin of the American Mathematical Society

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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 10.1112/jlms/s2-23.1.171

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).

Frank F. Bonsall and John Duncan, Complete normed algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80, Springer-Verlag, New York-Heidelberg, 1973. 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 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 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 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 10.1090/S0002-9904-1967-11735-X

Irving Kaplansky, Ring isomorphisms of Banach algebras, Canad. J. Math. 6 (1954), 374–381. MR 62960, DOI 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 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, London Mathematical Society Lecture Note Series, No. 21, Cambridge University Press, Cambridge-New York-Melbourne, 1976. 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 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