arXiv subjects
Publications and source records attributed to Farkhad Arzikulov.
It is proved that every 2-local derivation on an AW$^*$-algebra of type I is a derivation. Also an analog of Gleason theorem for signed measures on projections of homogenous AW$^*$-algebras except the cases of an AW$^*$-algebra of type I$_2$ and a factor of type I$_m$, $2<m<\infty$ is proved.
In the present paper we prove that every 2-local derivation on a von Neumann algebra of type I is a derivation.
In the present paper we prove that every 2-local derivation on a semi-finite von Neumann algebra is a derivation.
In the given article the notion of infinite norm decomposition of a C$^*$-algebra is investigated. The norm decomposition is some generalization of Peirce decomposition. It is proved that the infinite norm decomposition of any C$^*$-algebra is a C$^*$-algebra. C$^*$-factors with an infinite and a nonzero finite projection and simple purely infinite C$^*$-algebras are constructed.