Annals of Functional Analysis, ( ISI ), Volume (1), No (2), Year (2010-12) , Pages (103-111)

Title : ( δ, ε-DOUBLE DERIVATIONS ON BANACH ALGEBRAS )

Authors: Shirin Hejazian , hussein mahdavian rad , Madjid Mirzavaziri ,

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Let A be an algebra and let delta, sigma : A -> A be two linear mappings. A ( delta, sigma)-double derivation is a linear mapping d : A -> A satisfying d(ab) = d(a)b+ad(b)+ delta(a) sigma(b)+ sigma(a) delta(b) (a, b in A). We study some algebraic properties of these mappings and give a formula for calculating dn(ab). We show that if A is a Banach algebra such that either is semi-simple or every derivation from A into any Banach A-bimodule is continuous then every ( delta, sigma)- double derivation on A is continuous whenever so are  and . We also discuss the continuity of delta when d and sigma are assumed to be continuous.

Keywords

, derivation, ( sima, tau)-double derivation, automatic
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@article{paperid:1021134,
author = {Hejazian, Shirin and Mahdavian Rad, Hussein and Mirzavaziri, Madjid},
title = {δ, ε-DOUBLE DERIVATIONS ON BANACH ALGEBRAS},
journal = {Annals of Functional Analysis},
year = {2010},
volume = {1},
number = {2},
month = {December},
issn = {2008-8752},
pages = {103--111},
numpages = {8},
keywords = {derivation; ( sima; tau)-double derivation; automatic continuity},
}

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%0 Journal Article
%T δ, ε-DOUBLE DERIVATIONS ON BANACH ALGEBRAS
%A Hejazian, Shirin
%A Mahdavian Rad, Hussein
%A Mirzavaziri, Madjid
%J Annals of Functional Analysis
%@ 2008-8752
%D 2010

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