Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
MathSciNet review: 0370191
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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] 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46H05

Retrieve articles in all journals with MSC: 46H05

Additional Information

Keywords: Free semigroup, norm, spectrum
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society