Abstract
Let A be an operator algebra on a Hilbert space. We say that an element G ∈ A is an all-derivable point of A for the strong operator topology if every strong operator topology continuous derivable linear mapping φ at G (i.e. φ ( S T ) = φ ( S ) T + S φ ( T ) for any S , T ∈ alg N with S T = G ) is a derivation. Let N be a continuous nest on a complex and separable Hilbert space H. We show in this paper that every orthogonal projection operator P ( M ) ( 0 ≠ M ∈ N ) is an all-derivable point of alg N for the strong operator topology.
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