Abstract:

Let  τ(N) be any nest algebra on a complex and separable Hilbert space H, and (Φ,ψ)  be a pair of linear mappings of  τ(N).We prove that if  (Φ,ψ)  satisfies Φ(AB)=Φ(A)B+Aψ(B) for all A,B∈τ(N) with AB=0, then (Φ,ψ) is a pair of generalized inner derivations.

Key words: nest algebra; generalized derivation; a pair of generalized derivation