The spectrum of some special elements in the free Banach algebra
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- by Abdullah H. Al-Moajil PDF
- Proc. Amer. Math. Soc. 50 (1975), 218-222 Request permission
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 $\{ \lambda :|\lambda - f(e)| \leqslant {\Sigma _{\mathcal {S} \ne e}}|f(\mathcal {S})|\}$.References
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A. H. Al-Moajil, Nilpotency and quasipotency in Banach algebras, Ph.D. Dissertation, University of Oregon, Corvallis, Ore., 1973.
- Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
Additional Information
- © Copyright 1975 American Mathematical Society
- 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