La topologie de la convergence bornée sur les algèbres de fonctions continues
Linear topological properties of the Lumer-Smirnov class of the unit polydisc are studied. The topological dual and the Fréchet envelope are described. It is proved that has a weak basis but it is nonseparable in its original topology. Moreover, it is shown that the Orlicz-Pettis theorem fails for .
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,...