Let f be a split submersion between paracompact Banach manifolds. We obtain here various conditions for f to be a fiber bundle. First, we give general conditions in terms of path-liftings. As a… (More)

Weshow that ifX is a Banach space having an unconditional basis and a C p-smooth Lipschitz bump function, then for every C1-smooth functionf from X into a Banach space Y, and for every continuous… (More)

Estibalitz Durand-Cartagena, J. A. Jaramillo, Nageswari Shanmugalingam

2010

A useful feature of the Euclidean n-space, n ≥ 2, is the fact that every pair of points x and y can be joined not only by the line segment [x, y], but also by a large family of curves whose length is… (More)

For a large class of metric spaces with nice local structure, which includes Banach-Finsler manifolds and geodesic spaces of curvature bounded above, we give sufficient conditions for a local… (More)

Throughout, E, G, and F will be complex Banach spaces, E a subspace of G. The question which gave rise to the material reviewed here was first posed by Dineen [D1] in relation to holomorphic… (More)

We study the extension of bilinear forms from a given subspace of an L1 -space to the whole space. Precisely, an isomorphic embedding j: E → X is said to be (linearly) 2 -exact if bilinear forms on E… (More)

For a metric space X, we study the space D ∞ (X) of bounded functions on X whose infinitesimal Lipschitz constant is uniformly bounded. D ∞ (X) is compared with the space LIP ∞ (X) of bounded… (More)

We investigate the best order of smoothness of L p (L q). We prove in particular that there exists a C ∞-smooth bump function on L p (L q) if and only if p and q are even integers and p is a multiple… (More)

We study the global inversion of a continuous nonsmooth mapping f : R → R, which may be non-locally Lipschitz. To this end, we use the notion of pseudo-Jacobian map associated to f , introduced by… (More)