Víctor M. Sánchez

Sierpinski-Zygmund functions and other problems on lineability

We find large algebraic structures inside the following sets of pathological functions: (i) perfectly everywhere surjective functions, (ii) differentiable functions with almost nowhere continuous derivatives, (iii) differentiable nowhere monotone functions, and (iv) Sierpinski-Zygmund functions. The conclusions obtained on (i) and (iii) are improvements of some already known results.

DISJOINTLY STRICTLY-SINGULAR INCLUSIONS BETWEEN REARRANGEMENT INVARIANT SPACES

A linear operator between two Banach spaces X and Y is strictly-singular (or Kato) if it fails to be an isomorphism on any infinite dimensional subspace. A weaker notion for Banach lattices introduced in [8] is the following one: an operator T from a Banach lattice X to a Banach space Y is said to be disjointly strictly-singular if there is no disjoint sequence of non-null vectors (xn)n∈N in X such that the restriction of T to the subspace [(xn)∞n=1] spanned by the vectors (xn)n∈N is an isomorphism. Clearly every strictly-singular operator is disjointly strictly-singular but the converse is not true in general (consider for example the canonic inclusion Lq[0, 1]↪Lp[0, 1] for 1≤p<q<∞). In the special case of considering Banach lattices X with a Schauder basis of disjoint vectors both concepts coincide. The notion of disjointly strictly-singular has turned out to be a useful tool in the study of lattice structure of function spaces (cf. [7–9]). In general the class of all disjointly strictly-singular operators is not an operator ideal since it fails to be stable with respect to the composition on the right. The aim of this paper is to study when the inclusion operators between arbitrary rearrangement invariant function spaces E[0, 1] ≡ E on the probability space [0, 1] are disjointly strictly-singular operators.

Indices defined by interpolation scales and applications

We study inclusion indices relative to an interpolation scale. Applications are given to several families of functions spaces.

Fast growth of undoped and Sn- and Tb-doped ZnO nanowires by Joule heating of Zn

Joule heating of Zn wires by flowing a high electric current density has been used to grow, in times as short as tens of seconds, undoped and Sn- or Tb-doped ZnO nanowires. The contact of tin oxide powder with the starting Zn wire during heating leads to the growth of branched ZnO nanostructures by a catalytic effect of Sn. The growth treatment in the presence of terbium oxide gives rise to a complex ZnO arrangement of nanoparticles attached to nanowires, which show luminescence emission of Tb3+ transition due to the incorporation of a small amount of Tb into the ZnO nanoparticles during the growth process. The contribution of electromigration, associated with the high electric current density, to the rapid growth of the nanowires, as compared with other thermal-based techniques, is discussed.

The history of a general criterium on spaceability

Abstract There are just a few general criteria on spaceability. This survey paper is the history of one of the first ones. Let I1 and I2 be arbitrary operator ideals and E and F be Banach spaces. The spaceability of the set of operators I1(E, F)\ I2(E, F) is studied. Before stating the criterium, the paper summarizes the main results about lineability and spaceability of differences between particular operator ideals obtained in recent years. They are the seed of the ideas contained in the general criterium.

An approach to module binding by fuzzy partitioning

A new method for dealing with the problem of module selection on unscheduled behavioral descriptions is described. The method is based on the application to partitioning of some results of fuzzy set theory. It inherits, from its theoretical basis, some interesting properties, such as global treatment of similarity among operators, and computational simplicity.<<ETX>>