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1
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Prime and semiprime rings with symmetric skew n-derivations

100%
Fošner A.
Colloquium Mathematicum
|
2014
|
tom 134
|
nr 2
245-253
EN
Let n ≥ 3 be a positive integer. We study symmetric skew n-derivations of prime and semiprime rings and prove that under some certain conditions a prime ring with a nonzero symmetric skew n-derivation has to be commutative.
2
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2-local Jordan automorphisms on operator algebras

100%
Fošner A.
Studia Mathematica
|
2012
|
tom 209
|
nr 3
235-246
EN
We investigate 2-local Jordan automorphisms on operator algebras. In particular, we show that every 2-local Jordan automorphism of the algebra of all n× n real or complex matrices is either an automorphism or an anti-automorphism. The same is true for 2-local Jordan automorphisms of any subalgebra of ℬ which contains the ideal of all compact operators on X, where X is a real or complex separable Banach spaces and ℬ is the algebra of all bounded linear operators on X.
3
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Preserving zeros of Lie product on alternate matrices

64%
Fošner A., Kuzma B.
Special Matrices
|
2016
|
tom 4
|
nr 1
80-100
EN
We study continuous maps on alternate matrices over complex field which preserve zeros of Lie product.
4
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Nonlinear Lie-type derivations of von Neumann algebras and related topics

51%
Fošner A., Wei F., Xiao Z.
Colloquium Mathematicum
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2013
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tom 132
|
nr 1
53-71
EN
Motivated by the powerful and elegant works of Miers (1971, 1973, 1978) we mainly study nonlinear Lie-type derivations of von Neumann algebras. Let 𝓐 be a von Neumann algebra without abelian central summands of type I₁. It is shown that every nonlinear Lie n-derivation of 𝓐 has the standard form, that is, can be expressed as a sum of an additive derivation and a central-valued mapping which annihilates each (n-1)th commutator of 𝓐. Several potential research topics related to our work are also presented.
5
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A Kleinecke-Shirokov type condition with Jordan automorphisms

51%
Brešar M., Fošner A., Fošner M.
Studia Mathematica
|
2001
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tom 147
|
nr 3
237-242
EN
Let φ be a Jordan automorphism of an algebra 𝓐. The situation when an element a ∈ 𝓐 satisfies $1/2(φ(a) + φ^{-1}(a)) = a$ is considered. The result which we obtain implies the Kleinecke-Shirokov theorem and Jacobson's lemma.
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