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Proceedings of the American Mathematical Society

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

 

 

Some consequences of left invertibility


Authors: Scott H. Hochwald and Bernard B. Morrel
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0883410-1
Article copyright: © Copyright 1987 American Mathematical Society