Jesús A. Jaramillo

SYMMETRIC POLYNOMIALS ON REARRANGEMENT-INVARIANT FUNCTION SPACES

The exact representation of symmetric polynomials on Banach spaces with symmetric basis and also on separable rearrangement-invariant function spaces over [0, 1] and [0, infinity) is given. As a consequence of this representation it is obtained that, among these spaces, l(2n), L-2n[0, 1], L-2n[0, infinity) and L-2n[0, infinity) boolean AND L-2n[0, infinity) where n, nl are both integers are the only spaces that admit separating polynomials.

Extension of bilinear forms on Banach spaces

We study the extension of bilinear and multilinear forms from a given subspace of a Banach space to the whole space. Precisely, an isomorphic embedding j : E --> X is said to be (linearly) N-exact if N-linear forms on E can be (linear and continuously) extended to X through j. We present some necessary and sufficient conditions for j to be 2-exact, as well as several examples of 2-exact embeddings. We answer a problem of Zalduendo: in a cotype 2 space bilinear extendable and integral forms coincide.

Smoothness and Estimates of Sequences in Banach-Spaces

An upper bound for the order of smoothness of bump functions in Banach spaces without copy ofc0 is found in terms of lower and upper estimates of their sequences. It is also shown that everyC∞-smooth Banach space with symmetric basis either containsc0 or is isomorphic toℓ2n for some integern.

Renormings of L-p(L-q)

We investigate the best order of smoothness of

Algebras of real analytic functions: Homomorphisms and bounding sets

L^p(L^q)

Almost classical solutions of Hamilton-Jacobi equations

. We prove in particular that there exists a

Inversion of Nonsmooth Maps between Banach Spaces

C^\infty

Restricting open surjections

-smooth bump function on

A class of Hamilton–Jacobi equations on Banach–Finsler manifolds

L^p(L^q)

Lipschitz-type functions on metric spaces

if and only if