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Lie triple derivations on nest algebras

✍ Scribed by Fangyan Lu

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 102 KB
Volume: 280
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200410520

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✦ Synopsis

Abstract

Let δ be a Lie triple derivation from a nest algebra 𝒜 into an 𝒜‐bimodule ℳ︁. We show that if ℳ︁ is a weak* closed operator algebra containing 𝒜 then there are an element S ∈ ℳ︁ and a linear functional f on 𝒜 such that δ (A) = SA – AS + f (A)I for all A ∈ 𝒜, and if ℳ︁ is the ideal of all compact operators then there is a compact operator K such that δ (A) = KA – AK for all A ∈ 𝒜. As applications, Lie derivations and Jordan derivations on nest algebras are characterized. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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