A new approach to the study of graded Lie algebras is found. Using functional identities the problem of describing the structure of such algebras is reduced to the problem of describing the structure of graded associative algebras.

COBISS.SI-ID: 14974809

The linear span of all values of a noncommutative polynomial on an algebra is studied. The background behind this is Connes' embedding conjecture. The main novelty of the paper is finding the connection to Lie algebras. Using Lie skew-ideals the aforementioned linear span is described on central simple algebras.

COBISS.SI-ID: 15220825

We describe the general form of bijective orthogonality preserving maps on n-dimesional real vector space equipped with a pair of generalized indefinite inner products. The relations between the projective space and vector space versions of this result are examined.

COBISS.SI-ID: 15333721

We characterize surjective linear maps preserving semi-Fredholm operators in both directions on the algebra of all bounded linear operators on an infinite-dimensional separable complex Hilbert space. As an application we substantially improve a recently obtained characterization of linear preservers of generalized invertibility.

COBISS.SI-ID: 15058521

On a separable C*-algebra A every (completely) bounded map which preserves closed two-sided ideals can be approximated uniformly by elementary operators if and only if A is a finite direct sum of C*-algebras of continuous sections vanishing at $\infty$ of locally trivial C*-bundles of finite type.

COBISS.SI-ID: 15352921