  We investigate relations between symmetrizations of quasi-Banach function
spaces and constructions such as Calderon-Lozanovskii spaces, pointwise product
spaces and pointwise multipliers. We show that under reasonable assumptions the
symmetrization commutes with these operations. We determine also the spaces of
pointwise multipliers between Lorentz spaces and Cesaro spaces. Developed
methods may be regarded as an arithmetic of quasi-Banach function spaces and
proofs of Theorems 3, 4 and 6 give a kind of tutorial for these methods.
Finally, the above results will be used in proofs of some factorization
results.
