CHARACTERIZATIONS OF HIGHER DERIVATIONS AND JORDAN HIGHER DERIVATIONS ON CSL ALGEBRAS

Abstract

AbstractLet ℒ be a commutative subspace lattice and 𝒜=Alg ℒ. It is shown that every Jordan higher derivation from 𝒜 into itself is a higher derivation. We say that D=(δi)i∈ℕ is a higher derivable linear mapping at G if δn(AB)=∑ i+j=nδi(A)δj(B) for all n∈ℕ and A,B∈𝒜 with AB=G. We also prove that if D=(δi)i∈ℕ is a bounded higher derivable linear mapping at 0 from 𝒜 into itself and δn (I)=0 for all n≥1 , or D=(δi)i∈ℕ is a higher derivable linear mapping at I from 𝒜 into itself, then D=(δi)i∈ℕ is a higher derivation.