Proceedings of the American Mathematical Society

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

Author(s): Zoltán Sebestyén
Journal: Proc. Amer. Math. Soc. 130 (2002), 1993-1996.
MSC (2000): Primary 46H05, 46J05
Posted: December 20, 2001
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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.

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

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

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

DOI: 10.1090/S0002-9939-01-06278-5
PII: S 0002-9939(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
Posted: December 20, 2001
Dedicated: Dedicated to Professor Franek Szafraniec on the occasion of his sixtieth birthday
Communicated by: N. Tomczak-Jaegermann
Copyright of article: Copyright 2001, American Mathematical Society

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