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)

 
 

 

A seminorm with square property on a complex associative algebra is submultiplicative


Author: Zoltán Sebestyén
Journal: Proc. Amer. Math. Soc. 130 (2002), 1993-1996
MSC (2000): Primary 46H05, 46J05
DOI: https://doi.org/10.1090/S0002-9939-01-06278-5
Published electronically: December 20, 2001
MathSciNet review: 1896032
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The result stated in the title is proved as a consequence of an appropriate generalization replacing the square property of a seminorm with a similar weaker property which implies an equivalence to the supnorm of all continuous functions on a compact Hausdorff space also.


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

  • 1. R.Arens, M.Goldberg and W.A.J.Luxenburg, Multiplicative Factors for Seminorms II, J.Math.Anal.Appl. 170(1992), 401-413. MR 93k:46039
  • 2. B.Aupetit, Propriétés Spectrales des Algèbres de Banach, Lecture Notes in Math., vol. 735, Springer-Verlag, Berlin, Heidelberg and New York, 1979. MR 81i:46055
  • 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 92m:46068
  • 4. S.J.Bhatt, A seminorm with square property on a Banach algebra is submultiplicative, Proc.Amer.Math.Soc. 117(1993), 435-438. MR 93d:46072
  • 5. R.S.Doran and V.A.Belfi, Characterizations of ${\mathbb{C}}^*$-algebras: The Gelfand-Naimark Theorems, Pure and Applied Math. vol. 101, Marcel Decker, Inc., New York and Basel, 1986. MR 87k:46115
  • 6. Z.Magyar and Z.Sebestyén, On the definition of ${\mathbb{C}}^*$-algebras II, Can.J.Math. 37(1985), 664-681. MR 87b:46061
  • 7. T.W.Palmer, Banach Algebras and General Theory of $*$-Algebras, Vol. I, Cambridge Univ. Press, 1994. MR 95c:46002
  • 8. Z.Sebestyén, Every ${\mathbb{C}}^*$-seminorm is automatically submultiplicative, Period.Math.Hungar. 10(1979), 1-8. MR 80c:46065

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46H05, 46J05

Retrieve articles in all journals with MSC (2000): 46H05, 46J05


Additional Information

Zoltán Sebestyén
Affiliation: Department of Applied Analysis, Loránd Eötvös University, H-1053 Budapest, Kecskeméti u. 10-12, Hungary
Email: sebesty@cs.elte.hu

DOI: https://doi.org/10.1090/S0002-9939-01-06278-5
Keywords: Seminorm with the square property on an algebra, submultiplicative seminorm
Received by editor(s): September 6, 2000
Received by editor(s) in revised form: January 17, 2001
Published electronically: December 20, 2001
Dedicated: Dedicated to Professor Franek Szafraniec on the occasion of his sixtieth birthday
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society