Abstract
Suppose that A is an algebra and M is an A -bimodule. Let A be any element in A . A linear mapping δ from A into M is said to be derivable at A if δ ( ST ) = δ ( S ) T + S δ ( T ) for any S , T in A with ST = A . Given an algebra A , such as a non-abelian von Neumann algebra or an irreducible CDCSL algebra on a Hilbert space H with dimH ⩾ 2 , we show that there exists a nontrivial idempotent P in A such that for any Q ∈ P A P which is invertible in P A P , every linear mapping derivable at Q from A into some unital A -bimodule (for example, A or B ( H ) ) is derivation.
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