Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Automatic continuity of homomorphisms in topological algebras

Author: S. J. Bhatt
Journal: Proc. Amer. Math. Soc. 119 (1993), 135-139
MSC: Primary 46H40; Secondary 46J40
MathSciNet review: 1164140
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A homomorphism from a locally convex $ Q$-algebra to a uniform topological algebra is continuous. A one-to-one homomorphism from a regular complete spectrally bounded uniform topological algebra onto a dense subalgebra of a semisimple locally $ m$-convex $ Q$-algebra is open. Examples are discussed to show that none of the assumptions in these results can be omitted.

References [Enhancements On Off] (What's this?)

  • [1] G. R. Allan, A spectral theory for locally convex algebras, Proc. London Math. Soc. 15 (1965), 399-421. MR 0176344 (31:619)
  • [2] S. J. Bhatt, On spectra and numerical ranges in locally $ m$-convex algebras, Indian J. Pure Appl. Math. 14 (1983), 596-603. MR 709314 (85g:46057)
  • [3] S. J. Bhatt and D. J. Karia, Uniqueness of the uniform norm with an application to topological algebras, Proc. Amer. Math Soc. 116 (1992), 499-504. MR 1097335 (92m:46068)
  • [4] F. F. Bonsall and J. Duncan, Numerical ranges of operators on normed spaces and of elements of normed algebras, London Math. Soc. Lecture Notes Ser., vol. 2, Cambridge Univ. Press, Cambridge, New York, and Melbourne, 1971. MR 0288583 (44:5779)
  • [5] H. G. Dales, A discontinuous homomorphism from $ C(X)$, Amer. J. Math. 101 (1979), 647-734. MR 533196 (81g:46066)
  • [6] Maria Fragoulopoulou, Automatic continuity of$ ^{{\ast}}$morphisms between nor-normed topological $ ^{{\ast}}$algebras, Pacific J. Math. 14 (1991), 57-70. MR 1081674 (91m:46083)
  • [7] A. Guichardet, Special topics in topological algebras, Gordon and Breach, New York, London, and Paris, 1968. MR 0243351 (39:4673)
  • [8] R. Larsen, Banach algebras, Marcel Dekker, New York, 1973. MR 0487369 (58:7010)
  • [9] E. A. Michael, Locally multiplicatively convex topological algebras, Mem. Amer. Math. Soc., No. 11, Amer. Math. Soc., Providence, RI, 1952. MR 0051444 (14:482a)
  • [10] W. Rudin, Functional analysis, Tata-McGraw Hill, New Delhi, 1973. MR 0365062 (51:1315)
  • [11] S. Sakai, $ {C^{\ast}}$- and $ {W^{\ast}}$-algebras, Ergeb. Math. Grenzgeb., vol 60, Springer-Verlag, Berlin, Heidelberg, and New York, 1971.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46H40, 46J40

Retrieve articles in all journals with MSC: 46H40, 46J40

Additional Information

Keywords: Uniform seminorm, locally convex $ Q$-algebras, uniform algebras, regular algebras
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society