We prove three new dichotomies for Banach spaces a la W.T. Gowers` dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and ...

Using the method of forcing we construct a model for ZFC where CH does not hold and where there exists a connected compact topological space K of weight omega(1) < 2(omega) such that every operator on the Banach space of ...

We study Hahn-Banach extensions of multilinear forms defined on Banach sequence spaces. We characterize c0 in terms of extension of bilinear forms, and describe the Banach sequence spaces in which every bilinear form admits ...

The Semadeni derivative of a Banach space X, denoted by S(X), is the quotient of the space of all weak* sequentially continuous functionals in X** by the canon- ical copy of X. In a remarkable 1960 paper, Z. Semadeni ...

We analyse several examples of separable Banach spaces, some of them new, and relate them to several dichotomies obtained in [11], by classifying them according to which side of the dichotomies they fall.

This paper deals with the approximate solution of the following functional equation [formula presented] where f is a mapping from R into a normed vector space. We show stability results of this equation in quasi-β-Banach ...