Smooth norms in dense subspaces of Banach spaces

Antiproximinal Norms in Banach Spaces

We prove that every Banach space containing a complemented copy of c0 has an antiproximinal body for a suitable norm. If, in addition, the space is separable, there is a pair of antiproximinal norms. In particular, in a separable polyhedral space X, the set of all (equivalent) norms on X having an isomorphic antiproximinal norm is dense. In contrast, it is shown that there are no antiproximinal...

Strongly Proximinal Subspaces in Banach Spaces

We give descriptions of SSDand QP -points in C(K)-spaces and use this to characterize strongly proximinal subspaces of finite codimension in L1(μ). We provide some natural class of examples of strongly proximinal subspaces which are not necessarily finite codimensional. We also study transitivity of strong proximinal subspaces of finite codimension.

On quasi-complemented subspaces of banach spaces.

BANACH SPACES OF POLYNOMIALS AS “LARGE” SUBSPACES OF l∞-SPACES

In this note we study Banach spaces of traces of real polynomials on R to compact subsets equipped with supremum norms from the point of view of Geometric Functional Analysis.

Smooth Norms and Approximation in Banach

We prove two results about smoothness in Banach spaces of the type C(K). Both build upon earlier papers of the first named author [3,4]. We first establish a special case of a conjecture that remains open for general Banach spaces and concerns smooth approximation. We recall that a bump function on a Banach space X is a function β : X → R which is not identically zero, but which vanishes outsid...