LAUSR

ABSTRACT For a triangular algebra ???? and an automorphism σ of ????, we describe linear maps F,G:????→???? satisfying F(x)y+σ(x)G(y) = 0 whenever x,y∈???? are such that xy = 0. In particular, when ???? is a zero product determined triangular algebra, maps F and G satisfying the above condition are generalized skew derivations of the form F(x) = F(1)x+D(x) and G(x) = σ(x)G(1)+D(x) for all x∈????, where D:????→???? is a skew derivation. When ???? is not zero product determined, we show that there are also nonstandard solutions for maps F and G.