Maps preserving the ƛ-Lie product of operators

Let A be a standard operator algebra on a Banach space X with dimX ۲. In thispaper, we characterize the forms of additive maps on A which strongly preserve the squarezero of -Lie product of operators, i.e., if ϕ : A 􀀀! A is an additive map which satis es[A;B]۲ = ۰ ) [ϕ(A);B]۲ = ۰;for every A;B ۲ A and for a scalar number with ̸= 􀀀۱, then it is shown that there existsa function : A ! C such that ϕ(A) = (A)A, for every A ۲ A.

کلیدواژه ها:

Preserver problem ، Standard operator algebra ، -Lie product ، Lie product.