Some Consequences of Left Invertibility

Scott H. Hochwald

doi:10.2307/2046128

Some Consequences of Left Invertibility

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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 → 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.

Original language	American English
Journal	Proceedings of the American Mathematical Society
Volume	100
Issue number	1
DOIs	https://doi.org/10.2307/2046128
State	Published - May 1987

Keywords

Algebra

Disciplines

Algebra

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N2 - 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.

AB - 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.

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Some Consequences of Left Invertibility

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