Functional identities of degree 2 in CSL algebras

‎Let L be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space H with dimH≥3‎, ‎AlgL‎ ‎the CSL algebra associated with L and M be an algebra containing AlgL‎. ‎This article is aimed at describing the form of‎ ‎additive mapppings F1‎,‎F2‎,‎G1‎,‎G2:AlgL⟶M satisfying functional identity‎ ‎F1(X)Y+F2(Y)X+XG2(Y)+YG1(X)=0 for all X‎,‎Y∈AlgL‎. ‎As an application generalized inner biderivations and commuting‎ ‎additive mappings are determined‎.