The use of operators for the construction of normal bases for the space of continuous functions on .
The -deformation of the classical convolution
We study deformations of the classical convolution. For every invertible transformation T:μ ↦ Tμ, we are able to define a new associative convolution of measures by . We deal with the -deformation of the classical convolution. We prove the analogue of the classical Lévy-Khintchine formula. We also show the central limit measure, which turns out to be the standard Gaussian measure. Moreover, we calculate the Poisson measure in the -deformed classical convolution and give the orthogonal polynomials...
The -boundary of weighted spaces of holomorphic functions.
The van der Put base for -functions.
The variational approach to the Dirichlet problem in C*-algebras
The aim of this work is to develop the variational approach to the Dirichlet problem for generators of sub-Markovian semigroups on C*-algebras. KMS symmetry and the KMS condition allow the introduction of the notion of weak solution of the Dirichlet problem. We will then show that a unique weak solution always exists and that a generalized maximum principle holds true.
The Vitali convergence theorem for the vector-valued McShane integral
The classical Vitali convergence theorem gives necessary and sufficient conditions for norm convergence in the space of Lebesgue integrable functions. Although there are versions of the Vitali convergence theorem for the vector valued McShane and Pettis integrals given by Fremlin and Mendoza, these results do not involve norm convergence in the respective spaces. There is a version of the Vitali convergence theorem for scalar valued functions defined on compact intervals in given by Kurzweil and...
The von Neumann algebras generated by -gaussians
We study the -deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if is sufficiently close to , then these algebras do not depend on . In the same way, the notion of conditionally free von Neumann algebras often coincides with freeness.
The wavelet type systems
We consider biorthogonal systems of functions on the interval [0,1] or 𝕋 which have the same dyadic scaled estimates as wavelets. We present properties and examples of these systems.
The weak and strong convergence in metrizable spaces over valued fields.
The weak compactness of almost Dunford-Pettis operators
We characterize Banach lattices on which every positive almost Dunford-Pettis operator is weakly compact.
The weak distance between Banach spaces with a symmetric basis.
The weak Gelfand-Phillips property in spaces of compact operators
For Banach spaces and , let denote the space of all continuous compact operators from to endowed with the operator norm. A Banach space has the property if every Grothendieck subset of is relatively weakly compact. In this paper we study Banach spaces with property . We investigate whether the spaces and have the property, when and have the property.
The weak McShane integral
We present a weaker version of the Fremlin generalized McShane integral (1995) for functions defined on a -finite outer regular quasi Radon measure space into a Banach space and study its relation with the Pettis integral. In accordance with this new method of integration, the resulting integral can be expressed as a limit of McShane sums with respect to the weak topology. It is shown that a function from into is weakly McShane integrable on each measurable subset of if and only if...
The weak Phillips property
Let X be a Banach space. If the natural projection p:X*** → X* is sequentially weak*-weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.
The weak Radon-Nikodym property
The weak Radon-Nikodym property in Banach spaces
The Wiener Property for a Class of Discrete Hypergroups.
The Wiener transformation on the limits of symmetric spaces
The work of José Luis Rubio de Francia (II).
I am going to discuss the work José Luis Rubio did on weighted norm inequalities. Most of it is in the book we wrote together on the subject [12].
The work of José Luis Rubio de Francia (III).
The aim of this paper is to review a set of articles ([6], [10], [11], [13], [16], [25]) of which José Luis Rubio de Francia was author and co-author written between 1985 and 1987.