Catálogo de publicaciones - libros

The existence, uniqueness and continuous dependence of a mild solution of a semilinear impulsive functional-differential evolution nonlocal Cauchy problem in general Banach spaces are studied. Methods of fixed point theorems, of a semigroup of operators and the Banach contraction theorem are applied.

Complex Kähler polarizations are constructed for a class of real Banach-Lie algebras that are not necessarily *-algebras but include all the real compact *-algebras. The approach is based on the theory of spectral decompositions of Banach space operators, and particularly on Dunford scalar operators. The main results are illustrated by means of a family of examples that are constructed starting from the Schatten-von Neumann classes of Hilbert space operators C with ≥ 2.

Using a new characterization for subnormality of a commuting triple of operators (due to T. Trent, {xc[12]}, for single operators, extended by P. Găvruţă and N. Suciu, {xc[4]}, for commuting pairs) we shall give necessary and sufficient conditions on a triple indexed sequence of vectors from a Hilbert space such that it can be expressed as moments of an appropriate triple of commuting operators. We obtain an extension of Z. Sebestyén’s similar result ({xc[9]}, {xc[10]}) for simple sequences and D. Păunescu result ({xc[7]}, {xc[8]}) for double sequences. The analogue problem for triple indexed sequences of operators acting on a Hilbert space is also obtained.

C. Anantharaman-Delaroche and J. Renault have proved that the amenability of a topological locally compact groupoid implies the equality of the reduced and the full *-algebras. In this paper we shall prove the converse assertion under a technical hypothesis. We shall prove that if is a locally compact second countable groupoid endowed with a Haar system having ”a bounded decomposition over the principal groupoid associated to ”, then the equality * () = * () implies the amenability of all quasi-invariant measures. In order to prove this we shall see that the inequality for all Є () implies a similar inequality for all Є () (where Reg is the left regular representation of () on a quasi invariant measure μ, and is the trivial representation on μ).

In this paper, we extend the definition of the -numerical radius to Banach spaces. In order to do so, we use one of the classical characterizations of the classes, which can be naturally extended. Then, we give a first study of this concept. Some of the properties given in the Banach case are original, but most of them are a generalization of the Hilbert case, even if the proofs have to be done in completely different ways.

We give in this paper some asymptotic von Neumann inequalities for power bounded operators in the class and some spacial von Neumann inequalities associated with non zero elements of the point spectrum, when it is non void, of generalized Toeplitz operators. Introducing perturbed kernel, we consider classes which extend the classical classes . We give results about absolute continuity with respect to the Haar measure for operators in class . This allows us to give new results on cyclic vectors for such operators and provides invariant subspaces for their powers. Relationships between cyclic vectors for and involving generalized Toeplitz operators are given and the commutativity of {T}’, the commutant of is discussed.

We discuss two different approaches to the study of the long-time behavior of some disordered quantum anharmonic chains.

In {xc[3]} Gladyshev gave an interesting characterization of periodically correlatedness for the second-order one continuous time parameter univariate continuous stochastic processes, in terms of the support of an associated spectral bimeasure. Recently, Makagon {xc[6]} extended this result to the case, where continuity is weakened to locally square summability. It is our aim now to give such a characterization of periodically correlatedness for second order continuous time parameters infinite variate locally square integrable random fields.

This paper contains an analysis of weighted composition operators between Hardy and Bergman spaces of general simply-connected complex domains. Concepts studied include boundedness, compactness, boundedness below, isometry and invariant subspaces.

The paper characterizes the kernel functions on ℝ with the property that the associated convolution operators are controlled by certain maximal operators.