Originally this work served as the author's dissertation for the scientific title “Doctor of the
Hungarian Academy of Sciences”. To publish it in the form of a book has been initiated by …

Let θ: M→ N be a zero-product preserving linear map between algebras. We show that
under some mild conditions θ is a product of a central element and an algebra …

Several general techniques on linear preserver problems are described. The first one is
based on a transfer principle in Model Theoretic Algebra that allows one to extend linear …

We denote by Mn the algebra of all n× n complex matrices. A lot of attention has been
recently paid to linear preservers, that is, linear maps on Mn that preserve a certain subset or …

It is well known that every automorphism of the full matrix algebra is inner. We give a short
proof of this statement and discuss several extensions of this theorem including structural …

Commutativity preserving maps Page 1 Linear Algebra and its Applications 429 (2008) 1051–1070
Available online at www.sciencedirect.com www.elsevier.com/locate/laa Commutativity …

Let A and B be C*-algebras, let X be an essential Banach A-bimodule and let T: A→ B and
S: A→ X be continuous linear maps with T surjective. Suppose that T (a) T (b)+ T (b) T (a)= 0 …

Let Mn be the algebra of all n× n matrices over a commutative unital ring C, and let L be a C-
module. Various characterizations of bilinear maps {.,.}: Mn× Mn→ L with the property that {x …

In the present survey the main results of the theory of functional identities are presented and
an analysis of the current state of this theory is given. Applications obtained in this direction …

We characterize the bijective nonlinear maps of the set of all self-adjoint bounded linear
operators on a complex separable Hilbert space H of dimension at least 3 which preserve …