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Description Of 2-Local Two Sided Multiplication On An Algebra Of Matrices, Farhodjon N. Arzikulov, Kamola A. Solijanova

Scientific Bulletin. Physical and Mathematical Research

The present paper is devoted to 2-local derivation on associative and Jordan matrix rings. In 1997, P. Semrl introduced the notion of 2-local derivations and described 2-local derivations on the algebra ¬B(H) of all bounded linear operators on the infinite-dimensional separable Hilbert space H. A similar description for the finite-dimensional case appeared later in 2004. In the paper Y. Lin and T. Wong 2-local derivations have been described on matrix algebras over finite dimensional division rings. In 2012 Sh. Ayupov, K. Kudaybergenov suggested a new technique and have generalized the above mentioned results for abritrary Hilbert spaces. Namely they considered …