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Given a measurable space (Omega, mu) and a sequence of disjoint measurable subsets A = (A(n))(n), the associated averaging projection P-A and the orthogonal projection T-A are considered. We study the boundedness of these operators on variable e[...]texto impreso
García del Amo Jiménez, Alejandro José ; Hernández, Francisco L. ; Ruiz Bermejo, César | Cambridge University Press | 1996Interpolation properties of the class of disjointly strictly singular operators on Banach lattices are studied. We also give some applications to compare the lattice structure of two rearrangement invariant function spaces. In particular, we obt[...]texto impreso
In this paper, we study the existence of infinite dimensional closed linear subspaces of a rearrangement invariant space on [0,1] every nonzero element of which does not belong to any included rearrangement invariant space of the same class such[...]texto impreso
It is shown that a separable variable exponent (or Nakano) function space L-p(.)(?) has a lattice-isomorphic copy of l(q) if and only if q is an element of Rp(.), the essential range set of the exponent function p(.). Consequently Rp(.) is a lat[...]texto impreso
Hernández, Francisco L. ; Ruiz Bermejo, César ; Sánchez de los Reyes, Víctor Manuel | Elsevier | 2015-11Let I1 and I2 be arbitrary operator ideals in the sense of Pietsch and E and F be Banach spaces such that the set I1(E,F){set minus}I2(E,F) is non-empty. We give a quite general sufficient condition on the Banach spaces in order to obtain the sp[...]texto impreso
A Banach space X is subprojective if every infinite-dimensional subspace of X has a subspace which is complemented in X. We prove that separable Nakano sequence spaces l((pn)) are subprojective. Subprojectivity is also characterized in separable[...]texto impreso
A subset A of a Banach space is called Banach–Saks when every sequence in A has a Cesàro convergent subsequence. Our interest here focuses on the following problem: is the convex hull of a Banach–Saks set again Banach–Saks? By means of a combina[...]
