$σ$-Derivations in Banach Algebras

Details $σ$-Derivations in Banach Algebras $σ$-Derivations in Banach Algebras

2005-05-16

arxiv.org/abs/math/0505319v3

Bull. Iranian Math. Soc. 32 (2006), no. 1, 65-78

Mathematics

Functional Analysis

12 pages

Scientific paper

Introducing the notions of (inner) $\sigma$-derivation, (inner) $\sigma$-endomorphism and one-parameter group of $\sigma$-endomorphisms ($\sigma$-dynamics) on a Banach algebra, we correspond to each $\sigma$-dynamics a $\sigma$-derivation named as its $\sigma$-infinitesimal generator. We show that the $\sigma$-infinitesimal generator of a $\sigma$-dynamics of inner $\sigma$-endomorphisms is an inner $\sigma$-derivation and deal with the converse. We also establish a nice generalized Leibniz formula and extend the Kleinenckr--Sirokov theorem for $\sigma$-derivations under certain conditions.

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