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Prime and semiprime rings with symmetric skew n-derivations

Ajda Fošner — 2014

Colloquium Mathematicae

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-local Jordan automorphisms on operator algebras

Ajda Fošner — 2012

Studia Mathematica

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.

A note on local automorphisms

Ajda Fošner — 2006

Czechoslovak Mathematical Journal

Let $H$ be an infinite-dimensional almost separable Hilbert space. We show that every local automorphism of $ℬ (H)$ , the algebra of all bounded linear operators on a Hilbert space $H$ , is an automorphism.

Preserving zeros of Lie product on alternate matrices

Ajda Fošner; Bojan Kuzma — 2016

Special Matrices

We study continuous maps on alternate matrices over complex field which preserve zeros of Lie product.

A Kleinecke-Shirokov type condition with Jordan automorphisms

Matej Brešar; Ajda Fošner; Maja Fošner — 2001

Studia Mathematica

Let φ be a Jordan automorphism of an algebra . The situation when an element 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.

Nonlinear Lie-type derivations of von Neumann algebras and related topics

Ajda Fošner; Feng Wei; Zhankui Xiao — 2013

Colloquium Mathematicae

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...

Centralizing traces and Lie-type isomorphisms on generalized matrix algebras: a new perspective

Xinfeng Liang; Feng Wei; Ajda Fošner — 2019

Czechoslovak Mathematical Journal

Let $ℛ$ be a commutative ring, $𝒢$ be a generalized matrix algebra over $ℛ$ with weakly loyal bimodule and $𝒵 (𝒢)$ be the center of $𝒢$ . Suppose that $𝔮 : 𝒢 \times 𝒢 \to 𝒢$ is an $ℛ$ -bilinear mapping and that $𝔗_{𝔮} : 𝒢 \to 𝒢$ is a trace of $𝔮$ . The aim of this article is to describe the form of $𝔗_{𝔮}$ satisfying the centralizing condition $[𝔗_{𝔮} (x), x] \in 𝒵 (𝒢)$ (and commuting condition $[𝔗_{𝔮} (x), x] = 0$ ) for all $x \in 𝒢$ . More precisely, we will revisit the question of when the centralizing trace (and commuting trace) $𝔗_{𝔮}$ has the so-called proper form from a new perspective. Using the aforementioned...

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