On Extension of Bi-Derivations to the Bidual of Banach Algebras

On Extension of Bi-Derivations to the Bidual of Banach Algebras

We present some necessary and sufficient conditions such that the (Arens) extensions of a bi-derivation on Banach algebras are again bi-derivations. We then examine our results for some Banach algebras. In particular, we show that the (Arens) extensions of a bi-derivation on C*–algebras are bideriva...

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Veröffentlicht in:Filomat 2016-01, Vol.30 (8), p.2261-2267
Hauptverfasser: Attar, A. Erfanian, Barootkoob, S., Vishki, H.R. Ebrahimi
Format: Artikel
Sprache:eng
Schlagworte:
Adjoints
Algebra
Banach space
Commuting
Linear algebra
Linear transformations
Logical proofs
Mathematical theorems
Sufficient conditions
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Beschreibung
Zusammenfassung:We present some necessary and sufficient conditions such that the (Arens) extensions of a bi-derivation on Banach algebras are again bi-derivations. We then examine our results for some Banach algebras. In particular, we show that the (Arens) extensions of a bi-derivation on C*–algebras are biderivations. Some results on extensions of an inner bi-derivation are also included.
ISSN:0354-5180
2406-0933
DOI:10.2298/FIL1608261E