Showing papers in "Revista Matematica Complutense in 1993"

On Multilinear Mappings of Nuclear Type

Abstract: In [15] A. Pietsch remarked that the attempt to classify the nonlinear operators between Banach spaces should haVe its starting point in the study of the different classes of multilinear mappings. See also [4] and [19]. On the othcr side dxc research in the Theory of Infrnite Dimensional Holomorphy has dealt with several topological Vector spaces of ii-linear mappings. See [1], [3], [5], [6], [7], [8], [10], [11], [12], [13] and [14] arnong other articles. MotiVated by ¡bese facts we introduce in this paper the class of ii-linear rnappings of nuclear type (s;r1,...,r~). Wc may think ¡bern as the multilinear counterpart of the (n.+oo,q)-nuc]ear linear operators of Pietsch (see [16], Chapter 18) as well as the natural generalization of ¡be n-linear mappings of nuclear typc considered by C. Gupta in [10]. Naturaily we cannot forgive ¡bat the nuclear linear

Dunford-Pettis-like Properties of Continuous Vector Function Spaces

Abstract: In this paper, dic structure of sorne operator ideals A deftned on continuous ftrnction spaces is studied. Conditions are considered under which "Te A ami'dic representing measureof Ttakesvalues in X are equivalent for tite scaies ofp-converging (C,,) azul weakly- p-compacr (1V,,) operatora. The scale (2,, is intermediate between the ideala C,=U (unconditionally sununingoperators), and C.,wB (completely continuousoperators), which have been studied by several authors (Bombal, Cembranos, Rodriguez-Salinas, Saab). The dual scale 1V,, is intermediate between dic ideals K(cornpact operators) and VsQ~=W(weakly compact operators), and dic results presented have a close connection with those of Diestel, Nufiez and Seifert. 1. PRELIMINARIES In this paper, B(Z,X) denotes die space of ali bounded X-valued E- measurable functions; if I~~=oo,p* denotes tIte conjugate number of p; it p=I, li,. plays tIte role of c 0.

Answer to a Question by M. Feder about K(X,Y)

Abstract: We show tEat a Banach space E constructed by Hourgain-Delbaen in 1980 answers a question put by Feder in 1982 about spaces of conxpact oper- ators.

On Strongly Pettis Integrable Functions in Locally Convex Spaces

Abstract: Sorne characterizations have been given for ?he relative compactness of dic range of ?he indefinite Pettis integral of a function defined on a complete finite measure space with values in a quasicomplete Hausdorff locally convex space. It Itas been sliown tliat tlie indefinite Pettis integral has a relatively compact range if tIte functions is measurable by serninorni. Separation property has been defrned for a scalarly measurable function asid it Itas been proved that a function with tuis property is integrable by seminorni. For a bounded function another characterization has been given for the relative cornpactness of the range of ?lic indefinite Pettis integral. Dunford-Pettis-PhuIlips theorem has been generalized ?o locaiJy convex spaces and as a corollary of ibis tbeorem sorne results which are valid for Banach spaces Itave been extended to lo- cally convex spaces.

Positive Radial Solutions for Semilinear Biharmonic Equations in Annular Domains

Abstract: Wc study dic exisience of positive radial solutions of 11 2u=g(jxi)f(u) in an annulus with Dirichlet boundary conditions. We establish ibat te equation has at least one positive radially syrnrnetric solution on any an- nulus iff and g are nonnegative, g~0 andfis superlinear at zero and + ~. Wc also give a property of positive radial solutions.

Dunford-Pettis-like Properties of Projective and Natural Tensor Product Spaces

Abstract: Several properties of weakly p-sumniable sequences and of ?lic scale of p-converging operators (i.e., operators transforming weakly p-summable sequences into convergent sequences) in projective and natural tensor products with an 4, space are considered. The last section studies ?he Dunford-Peuis pro- perty of order p (le., every weakly compact operator is p-convergent) in ?hose spaces.

The Tensor Product of Triples as Multilinear Product

Abstract: In this paper we introduce a notion of multilinear product ibr triples in Set, which if it is given by a distributive law Ihen coincides with the one given by Hunge. Wc also demonstrate that the tensor product of two triples, if there exist, is an initial object jo a suitable category of multilinear products.

On the Behaviour of Generalized Solutions to Genuinly Nonlinear First Order Equations for SmaIl and Large Values of Time

Abstract: fle paper deala with ihe asyznpiohic hehaviour of generalized soluuons io nonlinear first order equations. With the aid of explicit variational representation one studies ihe decrease of solutions for a large time. And for ihe small time an asymptotics of dic perturbation's front is calculated.

Boundedness on Stochastic Petri Nets

Abstract: Stochastic Petri nets generalize the notionof queueing systems and are a useful tnodel in perfonnance evaiuation ofparaflel anO distributed systems. wc give necessary anO sufficient conditions for the boundedness of a stochastic process related to these nets.