The paper is devoted to 2-local higher derivations on some algebras. It is shown that continuous 2-local higher derivations on B(H), for an infinite dimensional separable Hilbert space H are higher derivations and each 2-local inner higher derivation on F(H) (the ideal of all finite-dimensional operators from B(H)) is a higher derivation. Also, we prove that every 2-local higher derivation from a commutative ∗-subalgebra of the matrix algebra Mn over C is a higher derivation.
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