On weakly compact operators.
Operadores débilmente compactos en espacios de funciones continuas con valores vectoriales, y la propiedad de Radon-Nykodim.
Operators from C*-algebras to Banach Spaces.
Operators into L1 of a vector measure and applications to Banach lattices.
Operators on spaces of vector-valued continuous functions.
Operator-valued functions of bounded semivariation and convolutions
The abstract Perron-Stieltjes integral in the Kurzweil-Henstock sense given via integral sums is used for defining convolutions of Banach space valued functions. Basic facts concerning integration are preseted, the properties of Stieltjes convolutions are studied and applied to obtain resolvents for renewal type Stieltjes convolution equations.
Optimal domains for kernel operators on [0,∞) × [0,∞)
Let T be a kernel operator with values in a rearrangement invariant Banach function space X on [0,∞) and defined over simple functions on [0,∞) of bounded support. We identify the optimal domain for T (still with values in X) in terms of interpolation spaces, under appropriate conditions on the kernel and the space X. The techniques used are based on the relation between linear operators and vector measures.
Order convergence of vector measures on topological spaces
Let be a completely regular Hausdorff space, a boundedly complete vector lattice, the space of all, bounded, real-valued continuous functions on , the algebra generated by the zero-sets of , and a positive linear map. First we give a new proof that extends to a unique, finitely additive measure such that is inner regular by zero-sets and outer regular by cozero sets. Then some order-convergence theorems about nets of -valued finitely additive measures on are proved, which extend...
Order properties of the space of finitely additive transition functions.
Order properties of the space of strongly additive transition functions.
Orthogonal Expansion of Vector-Valued Functions and Measures
P-adic Spaces of Continuous Functions I
Properties of the so called -complete topological spaces are investigated. Also, necessary and sufficient conditions are given so that the space of all continuous functions, from a zero-dimensional topological space to a non-Archimedean locally convex space , equipped with the topology of uniform convergence on the compact subsets of to be polarly barrelled or polarly quasi-barrelled.
P-adic Spaces of Continuous Functions II
Necessary and sufficient conditions are given so that the space of all continuous functions from a zero-dimensional topological space to a non-Archimedean locally convex space , equipped with the topology of uniform convergence on the compact subsets of , to be polarly absolutely quasi-barrelled, polarly -barrelled, polarly -barrelled or polarly -barrelled. Also, tensor products of spaces of continuous functions as well as tensor products of certain -valued measures are investigated.
Path integrals in finite sets
Pełczyński's Property (V) on spaces of vector-valued functions
Pettis integration
Physical states on quantum logics. I
Points extrémaux et propriétés de Radon-Nikodym dans les espaces de Fréchet dentables
Points fixes et théorèmes ergodiques dans les espaces L¹(E)
We prove that for each linear contraction T : X → X (∥T∥ ≤ 1), the subspace F = {x ∈ X : Tx = x} of fixed points is 1-complemented, where X is a suitable subspace of L¹(E*) and E* is a separable dual space such that the weak and weak* topologies coincide on the unit sphere. We also prove some related fixed point results.
Pointwise compactness and continuity of the integral.
In this paper we bring together the different known ways of establishing the continuity of the integral over a uniformly integrable set of functions endowed with the topology of pointwise convergence. We use these techniques to study Pettis integrability, as well as compactness in C(K) spaces endowed with the topology of pointwise convergence on a dense subset D in K.