In a reasonable setting, we shall prove a Gleason-Kahane-Zelazko type theorem for spaces of analytic functions (in several variables). Using this result, we shall classify operators between different spaces that preserve cyclicity w.r.t. the shift operator i.e. we identify all operators T between X and Y such that Tf is cyclic in Y whenever f is cyclic in X. In fact, we shall show that all such operators need to be weighted composition operators.  Such a result is already known to be true for a variety of spaces in one-variable setting, like the Hardy spaces, Dirichlet-type spaces, Bergman space etc. however most proofs are specific to the space of functions in consideration. The proof I present in this talk will be valid for all spaces X and Y that satisfy certain reasonable set of properties.