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$\sigma$-Derivations in Banach Algebras

M. Mirzavaziri·M. S. Moslehian
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Abstract

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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BibTeXRIS

M. Mirzavaziri, M. S. Moslehian. 2005-05-16. $\sigma$-Derivations in Banach Algebras. https://arxiv.org/abs/math/0505319

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