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Operators preserving ideals in C*-algebras

100%
S. Shul'Man V.
Studia Mathematica
|
1994
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tom 109
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nr 1
67-72
EN
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.
2
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Lie Derivations on Trivial Extension Algebras

100%
Mokhtari A. H., Moafian F., Vishki H. R. E.
Annales Mathematicae Silesianae
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2017
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tom 31
|
nr 1
141-153
EN
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.
3
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Erratum to: Congruences and Ideals in a Distributive Lattice with Respect to a Derivation

88%
Barzegar H.
Bulletin of the Section of Logic
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2019
|
tom 48
|
nr 1
EN
The present note is an Erratum for the two theorems of the paper "Congruences and ideals in a distributive lattice with respect to a derivation" by M. Sambasiva Rao.
4
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A note on semidirect sum of Lie algebras

63%
Ostrowski T.
Discussiones Mathematicae - General Algebra and Applications
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2013
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tom 33
|
nr 2
233-247
EN
In the paper there are investigated some properties of Lie algebras, the construction which has a wide range of applications like computer sciences (especially to computer visions), geometry or physics, for example. We concentrate on the semidirect sum of algebras and there are extended some theoretic designs as conditions to be a center, a homomorphism or a derivative. The Killing form of the semidirect sum where the second component is an ideal of the first one is considered as well.
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