Some Consequences of Left Invertibility

Scott H. Hochwald

doi:10.2307/2046128

Some Consequences of Left Invertibility

Scott H. Hochwald

Research output: Contribution to journal › Article › peer-review

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

Access to Document

10.2307/2046128License: Unspecified

Cite this

@article{193c836d694b4bb2aae5ef1f1d43d106,

title = "Some Consequences of Left Invertibility",

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",

author = "Hochwald, \{Scott H.\}",

note = "You have javascript disabled. In order to preview this item and view access options please enable javascript. 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.",

year = "1987",

month = may,

doi = "10.2307/2046128",

language = "American English",

volume = "100",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

number = "1",

}

TY - JOUR

T1 - Some Consequences of Left Invertibility

AU - Hochwald, Scott H.

N1 - You have javascript disabled. In order to preview this item and view access options please enable javascript. 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.

PY - 1987/5

Y1 - 1987/5

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.

KW - Algebra

UR - http://www.jstor.org/stable/2046128

U2 - 10.2307/2046128

DO - 10.2307/2046128

M3 - Article

SN - 0002-9939

VL - 100

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -

Some Consequences of Left Invertibility

Abstract

Keywords

Disciplines

Access to Document

Other files and links

Cite this