2-locl derivations on some C*-algebras

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In this paper, we introduce the concept of trace-open projections in the second dual A** of a C*-algebra A, and we show that if there is a faithful normal semi-finite trace T on A**, and 1 is a T-open projection, then each 2-local derivation D from A to A** is an inner derivartion. We also show that this theorem hold for approximately 2-local derivations when A** is finite as a von neumann algebra.