SMOOTH APPROXIMATIONS OF NORMS IN SEPARABLE BANACH SPACES

Analytic approximations of norms in separable 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...

Evolution inclusions in non separable Banach spaces

We study a Cauchy problem for non-convex valued evolution inclusions in non separable Banach spaces under Filippov type assumptions. We establish existence and relaxation theorems.

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...

Lfc Bumps on Separable Banach Spaces

In this note we construct a C∞-smooth, LFC (Locally depending on Finitely many Coordinates) bump function, in every separable Banach space admitting a continuous, LFC bump function.