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A seminorm with square property on a Banach algebra is submultiplicative
Author:
S. J. Bhatt
Journal:
Proc. Amer. Math. Soc. 117 (1993), 435-438
MSC:
Primary 46H05; Secondary 46J05
MathSciNet review:
1128724
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Abstract: The result stated in the title is proved in a Banach algebra and is used to discuss (i) commutativity criteria in normed algebras, (ii) uniqueness of the uniform norm in uniform Banach algebras, and (iii) existence of continuous multiplicative linear functionals on topological algebras together with a simple reduction of the Michael problem in Fréchet algebras. Submultiplicativity does not imply subadditivity in the presence of the square property.
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 and convex topological rings, Bull. Amer. Math. Soc. 52 (1946), 931-935. MR 0017524 (8:165d)
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- B. Aupetit, Properétés spectrales des algèbres de Banach, Lecture Notes in Math. vol. 735, Springer-Verlag, Berlin, Heidelberg, and New York, 1979. MR 549769 (81i:46055)
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- -, Numerical ranges of operators on normed spaces and of elements of normed algebras, London Math. Soc. Lecture Note Ser., vol. 2, London Math. Soc., Cambridge, 1971.
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 , Amer. J. Math. 101 (1979), 647-734. MR 533196 (81g:46066)
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- S. Sakai,
 -and  -algebras, Springer-Verlag, Berlin, Heidelberg, and New York, 1971. MR 0442701 (56:1082)
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- Z. Sebestyen, Every
 -seminorm is automatically submultiplicative, Period. Math Hunger. 10 (1979), 1-8. MR 506161 (80c:46065)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1993-1128724-8
PII:
S 0002-9939(1993)1128724-8
Keywords:
Seminorm with the square property on a Banach algebra,
submultiplicative seminorm,
Michael problem in Fréchet algebras
Article copyright:
© Copyright 1993 American Mathematical Society
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