A few last words on pointwise multipliers of Calderón--Lozanovskiĭ spaces

We will provide a complete description of the space $M(X_F,X_G)$ of pointwise multipliers between two Calderón–Lozanovskiĭ spaces $X_F$ and $X_G$ built upon a rearrangement invariant space $X$ and two Young functions $F$ and $G$. Meeting natural expectations, the space $M(X_F,X_G)$ turns out to be another Calderón–Lozanovskiĭ space $X_{G\ominus F}$ with $G\ominus F$ being the appropriately understood generalized Young conjugate of $G$ with respect to $F$. Nevertheless, our argument is not a mere transplantation of existing techniques and requires a rather delicate analysis of the interplay between the space $X$ and functions $F$ and $G$. Furthermore, as an example to illustrate applications, we will solve the factorization problem for Calderón–Lozanovskiĭ spaces. All this not only complements and improves earlier results (basically giving them the final touch), but also confirms the conjecture formulated by Kolwicz, Leśnik and Maligranda in [Pointwise multipliers of Calderón–Lozanovskiĭ spaces, Math. Nachr. 286 (2012), no. 8-9, 876–907]. We will close this work by formulating a number of open questions that outline a promising panorama for future research.