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Book Review
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Book Information
Author(s):
F. F. Bonsall and J. Duncan
Title:
Complete normed algebras
Additional book information:
Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80, Springer-Verlag, New York, Heidelberg, Berlin 1973, x+301 pp. $26.20
References:
- 1.
- J. C. Alexander, Compact Banach algebras, Proc. London Math. Soc. (3) 18 (1968), 1-18. MR 37 #4618. MR 229040
- 2.
- G. R. Allan, An extension of the Šilov-Arens-Calderón theorem, J. London Math. Soc. 44 (1969), 595-601. MR 39 #4678. MR 243356
- 3.
- W. Ambrose, Structure theorems for a special class of Banach algebras, Trans. Amer. Math. Soc. 57 (1945), 364-386. MR 7, 126. MR 13235
- 4.
- R. Arens and A. P. Calderón, Analytic functions of several Banach algebra elements, Ann. of Math. (2) 62 (1955), 204-216. MR 17, 177. MR 71735
- 5.
- F. F. Bonsall, Semi-algebras of continuous functions, Proc. London Math. Soc. (3) 10 (1960), 122-140; ibid (3) 12 (1962), 133-143; (3) 13 (1963), 51-70. MR 22 #2892; 24 #A2862; 26 #615. MR 112034
- 6.
- F. F. Bonsall and J. Duncan, Dual representations of Banach algebras, Acta Math. 117 (1967), 79-102. MR 34 #4929. MR 205094
- 7.
- F. F. Bonsall and J. Duncan, Dually irreducible representations of Banach algebras, Quart. J. Math. Oxford Ser. (2) 19 (1968), 97-111. MR 38 #535. MR 232209
- 8.
- F. F. Bonsall and A. W. Goldie, Annihilator algebras, Proc. London Math. Soc. (3) 4 (1954), 154-167. MR 15, 881. MR 61768
- 9.
- P. J. Cohen, Factorization in group algebras, Duke Math. J. 26 (1959), 199-205. MR 21 #3729. MR 104982
- 10.
- I. M. Gelfand, To the theory of normed rings, Dokl. Akad. Nauk. SSSR 23 (1939), 430-432; 25 (1939), 570-572, 573-574. MR 1, 330; 1, 331.
- 11.
- I. M. Gelfand, Normierte Ringe, Mat. Sb. 9 (1941), 3-24. MR 4726
- 12.
- P. R. Halmos, Capacity in Banach algebras, Indiana Univ. Math. J. 20 (1971), 855-863. MR 42 #3569. MR 268672
- 13.
- B. E. Johnson, The uniqueness of the (complete) norm topology, Bull. Amer. Math. Soc. 73 (1967), 537-539. MR 35 #2142. MR 211260
- 14.
- B. E. Johnson, Continuity of derivations on commutative algebras, Amer. J. Math. 91 (1969), 1-10. MR 39 #7433. MR 246127
- 15.
- B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972). MR 374934
- 16.
- B. E. Johnson, Approximate diagonals and cohomology of certain annihilator Banach algebras, Amer. J. Math. 94 (1972), 685-698. MR 317050
- 17.
- S. Mazur, Sur les anneaux linéaires, C. R. Acad. Sci. Paris 207 (1938), 1025-1027.
- 18.
- M. Nagumo, Einige analytische Untersuchungen in linearen metrischen Ringen, Japan J. Math. 13 (1936), 61-80.
- 19.
- J. von Neumann, Zur Algebra tier Funktionaloperatoren und Theorie der normalen Operatoren, Math. Ann. 102 (1929), 370-427.
- 20.
- T. W. Palmer, Characterizations of C*-algebras, Bull. Amer. Math. Soc. 74 (1968), 538-540. MR 36 #5709. MR 222659
- 21.
- C. E. Rickart, General theory of Banach algebras, Van Nostrand, University Series in Higher Math., Princeton, N.J., Reprinted (with corrections) by Robert Krieger Publ. Co., 1974. MR 22 #5903. MR 115101
- 22.
- G. E. Šilov, On the decomposition of a commutative normed ring in a direct sum of ideals, Mat. Sb. 32 (74) (1953), 353-364; English transl., Amer. Math. Soc. Transl. (2) 1 (1955), 37-48. MR 14, 884; 17, 512. MR 73946
- 23.
- I. M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 260-264. MR 16, 1125. MR 70061
- 24.
- I. Vidav, Eine metrische Kennzeichnung der selbstadjungierten Operatoren, Math. Z. 66 (1956), 121-128. MR 18, 912. MR 84733
- 25.
- L. Waelbroeck, Le calcul symbolique dans les algèbres commutatives, J. Math. Pures Appl. (9) 33 (1954), 147-186. MR 17, 513. MR 73953
- 26.
- K. Yosida, On the group embedded in the metrical complete ring. Japan. J. Math. 13 (1936), 459-472.
Additional Information:
Reviewer(s):
C. E.
Rickart
Review Information:
Journal:
Bull. Amer. Math. Soc.
81
(1975),
Part 1:514-522.
DOI:
10.1090/S0002-9904-1975-13727-X
PII:
S 0002-9904(1975)13727-X
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