ar X iv : m at h / 05 05 31 9 v 1 [ m at h . FA ] 1 6 M ay 2 00 5 σ - Derivations in Banach Algebras ∗
نویسنده
چکیده
Introducing the notions of (inner) σ-derivation, (inner) σ-endomorphism and oneparameter group of σ-endomorphisms (σ-dynamics) on a Banach algebra, we correspond to each σ-dynamics a σ-derivation named as its σ-infinitesimal generator. We show that the σ-infinitesimal generator of a σ-dynamics of inner σ-endomorphisms is an inner σ-derivation and deal with the converse. We also establish a nice generalized Leibniz formula and extend the Kleinencke-Sirokov theorem for σ-derivations under certain conditions. ∗AMS Subject Classification. Primary 47D06; secondary 47B47, 16W25.
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