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The spectrum of some special elements in the free Banach algebra


Author: Abdullah H. Al-Moajil
Journal: Proc. Amer. Math. Soc. 50 (1975), 218-222
MSC: Primary 46H05
DOI: https://doi.org/10.1090/S0002-9939-1975-0370191-5
MathSciNet review: 0370191
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Abstract: Let $ F$ be the free semigroup on two generators, and let $ e$ denote the empty word in $ F$. It is shown that if $ f \in l'(F)$ has the property that its support freely generates a subsemigroup of $ F$, then the spectrum of $ f$ in $ l'(F)$ is equal to $ \{ \lambda :\vert\lambda - f(e)\vert \leqslant {\Sigma _{\mathcal{S} \ne e}}\vert f(\mathcal{S})\vert\} $.


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

  • [1] A. H. Al-Moajil, Nilpotency and quasipotency in Banach algebras, Ph.D. Dissertation, University of Oregon, Corvallis, Ore., 1973.
  • [2] C. E. Rickart, General theory of Banach algebras, University Ser. in Higher Math., Van Nostrand, Princeton, N. J., 1960. MR 22 #5903. MR 0115101 (22:5903)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0370191-5
Keywords: Free semigroup, norm, spectrum
Article copyright: © Copyright 1975 American Mathematical Society

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