On integration in complete bornological locally convex spaces
A generalization of I. Dobrakov’s integral to complete bornological locally convex spaces is given.
On integration of vector functions with respect to vector measures
We study integration of Banach space-valued functions with respect to Banach space-valued measures. We focus our attention on natural extensions to this setting of the Birkhoff and McShane integrals. The corresponding generalization of the Birkhoff integral was first considered by Dobrakov under the name -integral. Our main result states that -integrability implies McShane integrability in contexts in which the later notion is definable. We also show that a function is measurable and McShane integrable...
On interpolation of bilinear operators by methods associated to polygons
Stabiliamo teoremi di interpolazione bilineare per una combinazione dei metodi di - e -interpolazione associati ai poligoni, e per il -metodo. Mostriamo che un simile risultato fallisce per il -metodo, e diamo applicazioni all'interpolazione di spazi di operatori.
On interpolation of tensor products of Banach spaces.
For the complex interpolation method, Kouba proved an important interpolation formula for tensor products of Banach spaces. We give a partial extension of this formula in the injective case for the Gustavsson?Peetre method of interpolation within the setting of Banach function spaces.
On interpolation of weighted -spaces and Ovchinnikov’s theorem
On interpolation with boundary conditions.
On introduction of two diffeomorphism invariant Colombeau algebras
Equivalent definitions of two diffeomorphism invariant Colombeau algebras introduced in [7] and [5] (Grosser et al.) are listed and some new equivalent definitions are presented. The paper can be treated as tools for proving in [8] the equality of both algebras.
On invariant elements for positive operators.
In the paper we study the existence of nonzero positive invariant elements for positive operators in Riesz spaces. The class of Riesz spaces for which the results are valid is large enough to contain all the Banach lattices with order continuous norms. All the results obtained in earlier works deal with positive operators in KB-spaces and in many of them the approach is based upon the use of Banach limits. The methods created for KB-spaces cannot be extended to our more general setting; that is...
On Invariants of Hirzebruch and Cheeger-Gromov.
On inverse-closed algebras of infinitely differentiable functions
On inverses of -convex mappings
In the first part of this paper, we prove that in a sense the class of bi-Lipschitz -convex mappings, whose inverses are locally -convex, is stable under finite-dimensional -convex perturbations. In the second part, we construct two -convex mappings from onto , which are both bi-Lipschitz and their inverses are nowhere locally -convex. The second mapping, whose construction is more complicated, has an invertible strict derivative at . These mappings show that for (locally) -convex mappings...
On Ishlinskij's model for non-perfectly elastic bodies
The main goal of the paper is to formulate some new properties of the Ishlinskii hysteresis operator , which characterizes e.g. the relation between the deformation and the stress in a non-perfectly elastic (elastico-plastic) material. We introduce two energy functionals and derive the energy inequalities. As an example we investigate the equation describing the motion of a mass point at the extremity of an elastico-plastic spring.
On Isolated Points in the Dual Spaces of Locally Compact Groups.
On isometric domains of positive operators on -spaces
On isometric domains of positive operators on orlicz spaces
On isometrical extension properties of function spaces
In this note, we prove that any “bounded” isometries of separable metric spaces can be represented as restrictions of linear isometries of function spaces and , where and denote the Hilbert cube and a Cantor set, respectively.
On isometries and compact operators between p-adic Banach spaces
On isometries in linear metric spaces
On isomorphic classification of tensor products [Book]
On isomorphism classes of spaces
We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces , the topological sums of Cantor cubes , with smaller than the first sequential cardinal, and intervals of ordinal numbers [0,α]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of spaces with ≥ ℵ₀ and α ≥ ω₁ are the trivial ones. This result leads to some elementary questions on large cardinals.