Resumen: This paper is devoted to several questions concerning linearizations of function spaces. We first consider the relation between linearizations of a given space when it is viewed as a function space over different domains. Then we study the problem of characterizing when a Banach function space admits a Banach linearization in a natural way. Finally, we consider
the relevance of compactness properties in linearizations, more precisely, the relation between different compactness properties of a mapping, and compactness of its associated linear operator.
Resumen: Several forms of the Dunford-Pettis property are studied, each related to a different mode of sequential convergence, and a different class of weakly compact functions. The relationship between these Dunford-Pettis properties is investigated, and the appearance of previously studied Dunford-Pettis properties is pointed out,
