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Continuity of derivations, intertwining maps, and cocycles from Banach algebras

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Continuity of derivations, intertwining maps, and cocycles from Banach algebras. / Dales, H.G.; Villena, A. R.
In: Journal of the London Mathematical Society, Vol. 63, No. 1, 02.2001, p. 215-225.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Dales, HG & Villena, AR 2001, 'Continuity of derivations, intertwining maps, and cocycles from Banach algebras', Journal of the London Mathematical Society, vol. 63, no. 1, pp. 215-225. https://doi.org/10.1112/S0024610700001770

APA

Dales, H. G., & Villena, A. R. (2001). Continuity of derivations, intertwining maps, and cocycles from Banach algebras. Journal of the London Mathematical Society, 63(1), 215-225. https://doi.org/10.1112/S0024610700001770

Vancouver

Dales HG, Villena AR. Continuity of derivations, intertwining maps, and cocycles from Banach algebras. Journal of the London Mathematical Society. 2001 Feb;63(1):215-225. doi: 10.1112/S0024610700001770

Author

Dales, H.G. ; Villena, A. R. / Continuity of derivations, intertwining maps, and cocycles from Banach algebras. In: Journal of the London Mathematical Society. 2001 ; Vol. 63, No. 1. pp. 215-225.

Bibtex

@article{68b4536921c24404b5c21e1d277127c1,
title = "Continuity of derivations, intertwining maps, and cocycles from Banach algebras",
abstract = "Let A be a Banach algebra, and let E be a Banach A-bimodule. A linear map S:A→E is intertwining if the bilinear mapFormulais continuous, and a linear map D:A→E is a derivation if δ1D=0, so that a derivation is an intertwining map. Derivations from A to E are not necessarily continuous.The purpose of the present paper is to prove that the continuity of all intertwining maps from a Banach algebra A into each Banach A-bimodule follows from the fact that all derivations from A into each such bimodule are continuous; this resolves a question left open in [1, p. 36]. Indeed, we prove a somewhat stronger result involving left- (or right-) intertwining maps.",
author = "H.G. Dales and Villena, {A. R.}",
year = "2001",
month = feb,
doi = "10.1112/S0024610700001770",
language = "English",
volume = "63",
pages = "215--225",
journal = "Journal of the London Mathematical Society",
issn = "0024-6107",
publisher = "Oxford University Press",
number = "1",

}

RIS

TY - JOUR

T1 - Continuity of derivations, intertwining maps, and cocycles from Banach algebras

AU - Dales, H.G.

AU - Villena, A. R.

PY - 2001/2

Y1 - 2001/2

N2 - Let A be a Banach algebra, and let E be a Banach A-bimodule. A linear map S:A→E is intertwining if the bilinear mapFormulais continuous, and a linear map D:A→E is a derivation if δ1D=0, so that a derivation is an intertwining map. Derivations from A to E are not necessarily continuous.The purpose of the present paper is to prove that the continuity of all intertwining maps from a Banach algebra A into each Banach A-bimodule follows from the fact that all derivations from A into each such bimodule are continuous; this resolves a question left open in [1, p. 36]. Indeed, we prove a somewhat stronger result involving left- (or right-) intertwining maps.

AB - Let A be a Banach algebra, and let E be a Banach A-bimodule. A linear map S:A→E is intertwining if the bilinear mapFormulais continuous, and a linear map D:A→E is a derivation if δ1D=0, so that a derivation is an intertwining map. Derivations from A to E are not necessarily continuous.The purpose of the present paper is to prove that the continuity of all intertwining maps from a Banach algebra A into each Banach A-bimodule follows from the fact that all derivations from A into each such bimodule are continuous; this resolves a question left open in [1, p. 36]. Indeed, we prove a somewhat stronger result involving left- (or right-) intertwining maps.

U2 - 10.1112/S0024610700001770

DO - 10.1112/S0024610700001770

M3 - Journal article

VL - 63

SP - 215

EP - 225

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 1

ER -