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