Push-outs of derivations
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Push-outs of derivations. / Grønbæk, Niels.
I: Proceedings of the Indian Academy of sciences. Mathematical sciences, Bind 118, Nr. 2, 2008, s. 235-243.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Push-outs of derivations
AU - Grønbæk, Niels
PY - 2008
Y1 - 2008
N2 - Let A be a Banach algebra and let X be a Banach A-bimodule. In studying H¹(A,X) it is often useful to extend agiven derivation D: A->X to a Banach algebra Bcontaining A as an ideal, thereby exploiting (or establishing)hereditary properties. This is usually done using (bounded/unbounded)approximate identities to obtain the extension as a limit of operatorsb->D(ba)-b.D(a), a in A, in an appropriate operator topology, themain point in the proof being to show that the limit map is in fact aderivation. In this paper we make clear which part of this approach isanalytic and which algebraic by presenting an algebraic scheme thatgives derivations in all situations at the cost of enlarging themodule. We use our construction to give improvements and shorterproofs of some resultsfrom the literatureand to give a necessary and sufficient condition that biprojectivity andbiflatness are inherited to ideals
AB - Let A be a Banach algebra and let X be a Banach A-bimodule. In studying H¹(A,X) it is often useful to extend agiven derivation D: A->X to a Banach algebra Bcontaining A as an ideal, thereby exploiting (or establishing)hereditary properties. This is usually done using (bounded/unbounded)approximate identities to obtain the extension as a limit of operatorsb->D(ba)-b.D(a), a in A, in an appropriate operator topology, themain point in the proof being to show that the limit map is in fact aderivation. In this paper we make clear which part of this approach isanalytic and which algebraic by presenting an algebraic scheme thatgives derivations in all situations at the cost of enlarging themodule. We use our construction to give improvements and shorterproofs of some resultsfrom the literatureand to give a necessary and sufficient condition that biprojectivity andbiflatness are inherited to ideals
M3 - Journal article
VL - 118
SP - 235
EP - 243
JO - Proceedings of the Indian Academy of Sciences: Mathematical Sciences
JF - Proceedings of the Indian Academy of Sciences: Mathematical Sciences
SN - 0253-4142
IS - 2
ER -
ID: 4360927