## On automatic continuity of homomorphisms

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- by A. Beddaa, S. J. Bhatt and M. Oudadess PDF
- Proc. Amer. Math. Soc.
**128**(2000), 1039-1045 Request permission

## Abstract:

Introducing a weaker notion of regularity in a topological algebra, we examine and improve an automatic continuity theorem given by the second author. Examples and applications are given.## References

- S. J. Bhatt and D. J. Karia,
*Uniqueness of the uniform norm with an application to topological algebras*, Proc. Amer. Math. Soc.**116**(1992), no.Â 2, 499â€“503. MR**1097335**, DOI 10.1090/S0002-9939-1992-1097335-4 - S. J. Bhatt,
*Automatic continuity of homomorphisms in topological algebras*, Proc. Amer. Math. Soc.**119**(1993), no.Â 1, 135â€“139. MR**1164140**, DOI 10.1090/S0002-9939-1993-1164140-0 - S. J. Bhatt and H. V. Dedania,
*Banach algebras with unique uniform norm*, Proc. Amer. Math. Soc.**124**(1996), no.Â 2, 579â€“584. MR**1301488**, DOI 10.1090/S0002-9939-96-03063-8 - Leonard Gillman and Meyer Jerison,
*Rings of continuous functions*, Graduate Texts in Mathematics, No. 43, Springer-Verlag, New York-Heidelberg, 1976. Reprint of the 1960 edition. MR**0407579** - Vo-Khac Khoan,
*Distributions Analyse de Fourier Operateurs aux dĂ©rivees partielles*, vol. T. 1, Vuibert, Paris, 1972. - R. J. Loy,
*Math. Reviews*, 93k:46042, p. 6116, Amer. Math. Soc., 1993. - Anastasios Mallios,
*Topological algebras. Selected topics*, North-Holland Mathematics Studies, vol. 124, North-Holland Publishing Co., Amsterdam, 1986. Notas de MatemĂˇtica [Mathematical Notes], 109. MR**857807** - Michael J. Meyer,
*The spectral extension property and extension of multiplicative linear functionals*, Proc. Amer. Math. Soc.**112**(1991), no.Â 3, 855â€“861. MR**1052578**, DOI 10.1090/S0002-9939-1991-1052578-X - P. Hebroni,
*Sur les inverses des Ă©lĂ©ments dĂ©rivables dans un anneau abstrait*, C. R. Acad. Sci. Paris**209**(1939), 285â€“287 (French). MR**14** - Jean Schmets,
*Espaces de fonctions continues*, Lecture Notes in Mathematics, Vol. 519, Springer-Verlag, Berlin-New York, 1976 (French). MR**0423058**, DOI 10.1007/BFb0079245 - WiesĹ‚aw Ĺ»elazko,
*Banach algebras*, Elsevier Publishing Co., Amsterdam-London-New York; PWNâ€”Polish Scientific Publishers, Warsaw, 1973. Translated from the Polish by Marcin E. Kuczma. MR**0448079**

## Additional Information

**A. Beddaa**- Affiliation: Ecole Normale Superieure, B.P. 5118 Takaddoum, Rabat, Moroc
**S. J. Bhatt**- Affiliation: Ecole Normale Superieure, B.P. 5118 Takaddoum, Rabat, Moroc
**M. Oudadess**- Affiliation: Ecole Normale Superieure, B.P. 5118 Takaddoum, Rabat, Moroc; Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, Gujarat, India
- Received by editor(s): September 10, 1997
- Received by editor(s) in revised form: May 18, 1998
- Published electronically: July 28, 1999
- Communicated by: Dale Alspach
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**128**(2000), 1039-1045 - MSC (1991): Primary 46H40; Secondary 46H05
- DOI: https://doi.org/10.1090/S0002-9939-99-05040-6
- MathSciNet review: 1625768