Smooth extension of functions on a certain class of non-separable Banach spaces

Smooth Functions and Partitions of Unity on Certain Banach Spaces

In an earlier paper [4], the author sketched a method, based on the use of “Talagrand operators”, for defining infinitely differentiable equivalent norms on the spaces C0(L) for certain locally compact, scattered spaces L. A special case of this result was that a C renorming exists on C0(L) for every countable locally compact L. Recently, Hájek [3] extended this result by showing that a real no...

On the range of the derivative of Gâteaux-smooth functions on separable Banach spaces

We prove that there exists a Lipschitz function from l into IR which is Gâteaux-differentiable at every point and such that for every x, y ∈ l, the norm of f (x) − f (y) is bigger than 1. On the other hand, for every Lipschitz and Gâteaux-differentiable function from an arbitrary Banach space X into IR and for every ε > 0, there always exists two points x, y ∈ X such that ‖f (x)−f (y)‖ is less ...

A New Class of Banach Sequence Spaces

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.

Approximation by Smooth Functions with No Critical Points on Separable Banach Spaces

We characterize the class of separable Banach spaces X such that for every continuous function f : X → R and for every continuous function ε : X → (0,+∞) there exists a C smooth function g : X → R for which |f(x)− g(x)| ≤ ε(x) and g′(x) 6= 0 for all x ∈ X (that is, g has no critical points), as those infinite dimensional Banach spaces X with separable dual X∗. We also state sufficient condition...