Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

When is a linear functional multiplicative?


Authors: M. Roitman and Y. Sternfeld
Journal: Trans. Amer. Math. Soc. 267 (1981), 111-124
MSC: Primary 46H20; Secondary 16A99
DOI: https://doi.org/10.1090/S0002-9947-1981-0621976-6
MathSciNet review: 621976
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove here by elementary arguments a generalization of a theorem by Gleason, Kahane and Żelazko: If $ \varphi $ is a linear functional on an algebra with unit $ A$ such that $ \varphi (1) = 1$ and $ \varphi (u) \ne 0$ for any invertible $ u$ in $ A$, then $ \varphi $ is multiplicative, provided the spectrum of each element in $ A$ is bounded. We present also other conditions which may replace the assumptions on $ A$ in the theorem above.


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

  • [1] E. Borel, Sur les zéros des fonctions entières, Acta. Math. 20 (1896), 357-396. MR 1554885
  • [2] N. Bourbaki, Commutative algebra, Addison-Wesley, Reading, Mass., 1972.
  • [3] A. M. Gleason, A characterization of maximal ideals, J. Analyse Math. 19 (1967), 171-172. MR 0213878 (35:4732)
  • [4] J. P. Kahane and W. Żelazko, A characterization of maximal ideals in commutative Banach algebras, Studia Math. 29 (1968), 339-343. MR 0226408 (37:1998)
  • [5] R. Nevanlinna, Le théorème de Picard-Borel, Chelsea, New York, 1974.
  • [6] W. Rudin, Functional analysis, McGraw-Hill, New York, 1973. MR 0365062 (51:1315)
  • [7] W. Żelazko, A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math. 30 (1968), 83-85. MR 0229042 (37:4620)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46H20, 16A99

Retrieve articles in all journals with MSC: 46H20, 16A99


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0621976-6
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society