Works of Husain and others on the automatic continuity of characters

M. El Azhari

doi:10.15330/ms.45.2.205-212

We give a survey of Husain, Ng and Liang's results concerning the automatic continuity of algebra homomorphisms.We also give the improvements obtained by Joseph, Akkar, Oudadess, Zelazko and ourselves.

1. M. Akkar, Sur la structure des alg`ebres topologiques localement multiplicativement convexes, C. R. Acad. Sc. Paris, 279 (1974), Serie A, 941–944.

2. M. Akkar, M. El Azhari, M. Oudadess, Theor`emes de structure sur certaines alg`ebres de Frechet, Ann. Sc. Math. Quebec, 11 (1987), 245–252.

3. M. Akkar, M. El Azhari, M. Oudadess, Continuite des caract`eres dans les alg`ebres de Frechet `a bases, Canad. Math. Bull., 31 (1988), 168–174.

4. G.R. Allan, A spectral theory for locally convex algebras, Proc. London Math. Soc., 15 (1965), 399–421.

5. R. Arens, Dense inverse limit rings, Michigan Math. J., 5 (1958), 169–182.

6. T. Husain, Infrasequential topological algebras, Canad. Math. Bull., 22 (1979), 413–418.

7. T. Husain, Positive functionals on topological algebras with bases, Math. Japonica, 28 (1983), 683–687.

8. T. Husain, J. Liang, Multiplicative functionals on Frechet algebras with bases, Canad. J. Math., 29 (1977), 270–276.

9. T. Husain, J. Liang, Continuity of multiplicative linear functionals on Frechet algebras with bases, Bull. Soc. Roy. Sc. Li`ege, 46 (1977), 8–11.

10. T. Husain, S.B. Ng, Boundedness of multiplicative linear functionals, Canad. Math. Bull., 17 (1974), 213–215.

11. T. Husain, S.B. Ng, On continuity of algebra homomorphism and uniqueness of metric topology, Math. Zeit., 139 (1974), 1–4.

12. T. Husain, S.B. Ng, On the boundedness of multiplicative and positive functionals, J. Austral. Math. Soc., 21 (1976), 498–503.

13. T. Husain, S. Watson, Topological algebras with orthogonal Schauder bases, Pacific J. Math., 91 (1980), 339–347.

14. T. Husain, S. Watson, Algebras with unconditional orthogonal bases, Proc. Amer. Math. Soc., 79 (1980), 539–545.

15. G.A. Joseph, Multiplicative functionals and a class of topological algebras, Bull. Austral. Math. Soc., 17 (1977), 391–399.

16. E.A. Michael, Locally multiplicatively convex topological algebras, Mem. Amer. Math. Soc., 11 (1952).

17. S.B. Ng, S. Warner, Continuity of positive and multiplicative functionals, Duke Math. J., 39 (1972), 281–284.

18. M. Oudadess, Rayon de regularite dans les alg`ebres infrasequentielles, Canad. J. Math., 36 (1984), 84–94.

19. Do. Sin. Sya, On semi normed rings with an involution, Izv. Akad. Nauk. SSSR, 23 (1959), 509–528.

20. W. Zelazko, Functional continuity of commutative m-convex $B_0$-algebras with countable maximal ideal spaces, Colloq. Math., 51 (1987), 395–399.

	Works of Husain and others on the automatic continuity of characters
Author	M. El Azhari mohammed.elazhari@yahoo.fr Ecole Normale Superieure, Avenue Oued Akreuch, Takaddoum, Rabat, Morocco
Abstract	We give a survey of Husain, Ng and Liang's results concerning the automatic continuity of algebra homomorphisms.We also give the improvements obtained by Joseph, Akkar, Oudadess, Zelazko and ourselves.
Keywords	automatic continuity; algebra homomorphisms
DOI	doi:10.15330/ms.45.2.205-212
Reference	1. M. Akkar, Sur la structure des alg`ebres topologiques localement multiplicativement convexes, C. R. Acad. Sc. Paris, 279 (1974), Serie A, 941–944. 2. M. Akkar, M. El Azhari, M. Oudadess, Theor`emes de structure sur certaines alg`ebres de Frechet, Ann. Sc. Math. Quebec, 11 (1987), 245–252. 3. M. Akkar, M. El Azhari, M. Oudadess, Continuite des caract`eres dans les alg`ebres de Frechet `a bases, Canad. Math. Bull., 31 (1988), 168–174. 4. G.R. Allan, A spectral theory for locally convex algebras, Proc. London Math. Soc., 15 (1965), 399–421. 5. R. Arens, Dense inverse limit rings, Michigan Math. J., 5 (1958), 169–182. 6. T. Husain, Infrasequential topological algebras, Canad. Math. Bull., 22 (1979), 413–418. 7. T. Husain, Positive functionals on topological algebras with bases, Math. Japonica, 28 (1983), 683–687. 8. T. Husain, J. Liang, Multiplicative functionals on Frechet algebras with bases, Canad. J. Math., 29 (1977), 270–276. 9. T. Husain, J. Liang, Continuity of multiplicative linear functionals on Frechet algebras with bases, Bull. Soc. Roy. Sc. Li`ege, 46 (1977), 8–11. 10. T. Husain, S.B. Ng, Boundedness of multiplicative linear functionals, Canad. Math. Bull., 17 (1974), 213–215. 11. T. Husain, S.B. Ng, On continuity of algebra homomorphism and uniqueness of metric topology, Math. Zeit., 139 (1974), 1–4. 12. T. Husain, S.B. Ng, On the boundedness of multiplicative and positive functionals, J. Austral. Math. Soc., 21 (1976), 498–503. 13. T. Husain, S. Watson, Topological algebras with orthogonal Schauder bases, Pacific J. Math., 91 (1980), 339–347. 14. T. Husain, S. Watson, Algebras with unconditional orthogonal bases, Proc. Amer. Math. Soc., 79 (1980), 539–545. 15. G.A. Joseph, Multiplicative functionals and a class of topological algebras, Bull. Austral. Math. Soc., 17 (1977), 391–399. 16. E.A. Michael, Locally multiplicatively convex topological algebras, Mem. Amer. Math. Soc., 11 (1952). 17. S.B. Ng, S. Warner, Continuity of positive and multiplicative functionals, Duke Math. J., 39 (1972), 281–284. 18. M. Oudadess, Rayon de regularite dans les alg`ebres infrasequentielles, Canad. J. Math., 36 (1984), 84–94. 19. Do. Sin. Sya, On semi normed rings with an involution, Izv. Akad. Nauk. SSSR, 23 (1959), 509–528. 20. W. Zelazko, Functional continuity of commutative m-convex $B_0$-algebras with countable maximal ideal spaces, Colloq. Math., 51 (1987), 395–399.
Pages	205-212
Volume	45
Issue	2
Year	2016
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html