et A and B be Banach algebras. Linear operators T : A \\longrightarrow B with the property that T(a)T(b) = ? whenever a, b \\in A are such that ab = ? have been studied over the years and by many authors. They are usually considered under the name Lamperti operators or separating maps or disjointness preserving map or zero product preserving maps. The most common and natural way is to consider literally the same condition, that is, ab = ? \\Longrightarrow T(a)T(b) = ? (a, b \\in A), where T is a linear map between algebras A and B. Usually such operators are called zero product preserving maps.
