Shavkat Ayupov

2-Local derivations on von Neumann algebras

The paper is devoted to the description of 2-local derivations on von Neumann algebras. Earlier it was proved that every 2-local derivation on a semi-finite von Neumann algebra is a derivation. In this paper, using the analogue of Gleason Theorem for signed measures, we extend this result to type

2-LOCAL DERIVATIONS ON SEMI-FINITE VON NEUMANN ALGEBRAS

III

Innerness of continuous derivations on algebras of measurable operators affiliated with finite von Neumann algebras

III von Neumann algebras. This implies that on arbitrary von Neumann algebra each 2-local derivation is a derivation.

Spatiality of Derivations on the Algebra of τ-Compact Operators

The paper is devoted to so-called local and 2-local derivations on the noncommutative Arens algebra Lω(M,τ) associated with a von Neumann algebra M and a faithful normal semi-finite trace τ. We prove that every 2-local derivation on Lω(M,τ) is a spatial derivation, and if M is a finite von Neumann algebra, then each local derivation on Lω(M,τ) is also a spatial derivation and every 2-local derivation on M is in fact an inner derivation.

Topologies on central extensions of von Neumann algebras

In the present paper we prove that every 2-local derivation on a semi- finite von Neumann algebra is a derivation.

Jordan counterparts of Rickart and Baer \(*\)-algebras, II

Abstract The paper is devoted to 2-local derivations on matrix algebras over commutative regular algebras. We give necessary and sufficient conditions on a commutative regular algebra to admit 2-local derivations which are not derivations. We prove that every 2-local derivation on a matrix algebra over a commutative regular algebra is a derivation. We apply these results to 2-local derivations on algebras of measurable and locally measurable operators affiliated with type I von Neumann algebras.

Derivations on the Algebra of τ-Compact Operators Affiliated with a Type I von Neumann Algebra

Abstract This paper is devoted to derivations on the algebra S ( M ) of all measurable operators affiliated with a finite von Neumann algebra M . We prove that if M is a finite von Neumann algebra with a faithful normal semi-finite trace τ , equipped with the locally measure topology t , then every t -continuous derivation D : S ( M ) → S ( M ) is inner. A similar result is valid for derivation on the algebra S ( M , τ ) of τ -measurable operators equipped with the measure topology t τ .

Cartan Subalgebras, Weight Spaces, and Criterion of Solvability of Finite Dimensional Leibniz Algebras

This paper is devoted to derivations on the algebra S0(M, τ) of all τ-compact operators affiliated with a von Neumann algebra M and a faithful normal semi-finite trace τ. The main result asserts that every tτ-continuous derivation