Bulletin of the American Mathematical Society

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Authors: 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.

J. C. Alexander, Compact Banach algebras, Proc. London Math. Soc. (3) 18 (1968), 1–18. MR 229040, DOI 10.1112/plms/s3-18.1.1

G. R. Allan, An extension of the Silov-Arens-Calderón theorem, J. London Math. Soc. 44 (1969), 595–601. MR 243356, DOI 10.1112/jlms/s1-44.1.595

Warren Ambrose, Structure theorems for a special class of Banach algebras, Trans. Amer. Math. Soc. 57 (1945), 364–386. MR 13235, DOI 10.1090/S0002-9947-1945-0013235-8

Richard Arens and A. P. Calderón, Analytic functions of several Banach algebra elements, Ann. of Math. (2) 62 (1955), 204–216. MR 71735, DOI 10.2307/1969675

F. F. Bonsall, Semi-algebras of continuous functions, Proc. London Math. Soc. (3) 10 (1960), 122–140. MR 112034, DOI 10.1112/plms/s3-10.1.122

F. F. Bonsall and J. Duncan, Dual representations of Banach algebras, Acta Math. 117 (1967), 79–102. MR 205094, DOI 10.1007/BF02395041

F. F. Bonsall and J. Duncan, Dually irreducible representations of Banach algebras, Quart. J. Math. Oxford Ser. (2) 19 (1968), 97–111. MR 232209, DOI 10.1093/qmath/19.1.97

F. F. Bonsall and A. W. Goldie, Annihilator algebras, Proc. London Math. Soc. (3) 4 (1954), 154–167. MR 61768, DOI 10.1112/plms/s3-4.1.154

Paul J. Cohen, Factorization in group algebras, Duke Math. J. 26 (1959), 199–205. 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.

I. Gelfand, Normierte Ringe, Rec. Math. [Mat. Sbornik] N. S. 9 (51) (1941), 3–24 (German, with Russian summary). MR 0004726

P. R. Halmos, Capacity in Banach algebras, Indiana Univ. Math. J. 20 (1970/71), 855–863. MR 268672, DOI 10.1512/iumj.1971.20.20067

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

B. E. Johnson, Continuity of derivations on commutative algebras, Amer. J. Math. 91 (1969), 1–10. MR 246127, DOI 10.2307/2373262

Barry Edward Johnson, Cohomology in Banach algebras, Memoirs of the American Mathematical Society, No. 127, American Mathematical Society, Providence, R.I., 1972. MR 0374934

B. E. Johnson, Approximate diagonals and cohomology of certain annihilator Banach algebras, Amer. J. Math. 94 (1972), 685–698. MR 317050, DOI 10.2307/2373751

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.

T. W. Palmer, Characterizations of $C^{\ast }$-algebras, Bull. Amer. Math. Soc. 74 (1968), 538–540. MR 222659, DOI 10.1090/S0002-9904-1968-11998-6

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

G. E. Šilov, On the decomposition of a commutative normed ring into a direct sum of ideals, Amer. Math. Soc. Transl. (2) 1 (1955), 37–48. MR 0073946, DOI 10.1090/trans2/001/03

I. M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 260–264. MR 70061, DOI 10.1007/BF01362370

Ivan Vidav, Eine metrische Kennzeichnung der selbstadjungierten Operatoren, Math. Z. 66 (1956), 121–128 (German). MR 84733, DOI 10.1007/BF01186601

L. Waelbroeck, Le calcul symbolique dans les algèbres commutatives, J. Math. Pures Appl. (9) 33 (1954), 147–186 (French). MR 73953

26.

K. Yosida, On the group embedded in the metrical complete ring. Japan. J. Math. 13 (1936), 459-472.

1.

J. C. Alexander, Compact Banach algebras, Proc. London Math. Soc. (3) 18 (1968), 1-18. MR 37 #4618. MR 0229040

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.