Some consequences of left invertibility
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- by Scott H. Hochwald and Bernard B. Morrel PDF
- Proc. Amer. Math. Soc. 100 (1987), 109-110 Request permission
Abstract:
Let $A$ be a noncommutative Banach algebra with identity $e$. Let $L$ be a multiplicative semigroup of left-invertible elements of $A$ which properly contains the invertible elements of $A$. Then there does not exist a function $g:L \to A$ such that $g(ab) = g(b)g(a)$ and $g(a)a = e$ for all elements $a$ and $b$ of $L$. This paper contains an elementary proof of this result, and thereby answers a question posed by G. R. Allan.References
- G. R. Allan, Holomorphic left-inverse functions, Proceedings of the conference on Banach algebras and several complex variables (New Haven, Conn., 1983) Contemp. Math., vol. 32, Amer. Math. Soc., Providence, RI, 1984, pp. 7–14. MR 769494, DOI 10.1090/conm/032/769494
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 109-110
- MSC: Primary 46H05
- DOI: https://doi.org/10.1090/S0002-9939-1987-0883410-1
- MathSciNet review: 883410