Article
Some Consequences of Left Invertibility
Proceedings of the American Mathematical Society
(1987)
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 → 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.
Keywords
- Algebra
Disciplines
Publication Date
May, 1987
DOI
10.2307/2046128
Citation Information
Scott H. Hochwald. "Some Consequences of Left Invertibility" Proceedings of the American Mathematical Society Vol. 100 Iss. 1 (1987) p. 109 - 110 ISSN: 0002-9939 Available at: http://works.bepress.com/scott_hochwald/2/