Displaying similar documents to “A structure theorem Lie algebras of unbounded derivations in C * -algebras”

Lie Derivations on Trivial Extension Algebras

Amir Hosein Mokhtari, Fahimeh Moafian, Hamid Reza Ebrahimi Vishki (2017)

Annales Mathematicae Silesianae

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In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be expressed as a sum of a derivation and a center valued map vanishing at commutators. We then apply our results for triangular algebras. Some illuminating examples are also included.

Generalized derivations of Lie triple systems

Jia Zhou, Liangyun Chen, Yao Ma (2016)

Open Mathematics

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In this paper, we present some basic properties concerning the derivation algebra Der (T), the quasiderivation algebra QDer (T) and the generalized derivation algebra GDer (T) of a Lie triple system T, with the relationship Der (T) ⊆ QDer (T) ⊆ GDer (T) ⊆ End (T). Furthermore, we completely determine those Lie triple systems T with condition QDer (T) = End (T). We also show that the quasiderivations of T can be embedded as derivations in a larger Lie triple system.

Compactness of derivations from commutative Banach algebras

Matthew J. Heath (2010)

Banach Center Publications

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We consider the compactness of derivations from commutative Banach algebras into their dual modules. We show that if there are no compact derivations from a commutative Banach algebra, A, into its dual module, then there are no compact derivations from A into any symmetric A-bimodule; we also prove analogous results for weakly compact derivations and for bounded derivations of finite rank. We then characterise the compact derivations from the convolution algebra ℓ¹(ℤ₊) to its dual. Finally,...

Lie derivations of dual extensions of algebras

Yanbo Li, Feng Wei (2015)

Colloquium Mathematicae

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Let K be a field and Γ a finite quiver without oriented cycles. Let Λ := K(Γ,ρ) be the quotient algebra of the path algebra KΓ by the ideal generated by ρ, and let 𝒟(Λ) be the dual extension of Λ. We prove that each Lie derivation of 𝒟(Λ) is of the standard form.

Operators preserving ideals in C*-algebras

V. Shul'Man (1994)

Studia Mathematica

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The aim of this paper is to prove that derivations of a C*-algebra A can be characterized in the space of all linear continuous operators T : A → A by the conditions T(1) = 0, T(L∩R) ⊂ L + R for any closed left ideal L and right ideal R. As a corollary we get an extension of the result of Kadison [5] on local derivations in W*-algebras. Stronger results of this kind are proved under some additional conditions on the cohomologies of A.