Convexity and Haar null sets

It is shown that for every closed, convex and nowhere dense subset of a superreflexive Banach space there exists a Radon probability measure on so that for all . In particular, closed, convex, nowhere dense sets in separable superreflexive Banach spaces are Haar null. This is unlike the situation in separable nonreflexive Banach spaces, where there always exists a closed convex nowhere dense set which is not Haar null.

     

On The Homotopy Type of

We consider the homotopy type of classifying spaces , where is a finite -group, and we study the question whether or not the mod cohomology of , as an algebra over the Steenrod algebra together with the associated Bockstein spectral sequence, determine the homotopy type of . This article is devoted to producing some families of finite 2-groups where cohomological information determines the homotopy type of .

     

On the smoothness of the moduli space of mathematical instanton bundles

In this paper we prove that the moduli spaces MI _2n+1(k) of mathematical instanton bundles on ²ⁿ⁺¹ with quantum number k are singular for n 2 and k 3 ,giving a positive answer to a conjecture made by Ancona and Ottaviani in 1993.     

Λ0-Nuclear Operators and Λ0-Nuclear Spaces in p-adic Analysis

For a Köthe sequence space, the classes of ₀-nuclear spaces and spaces with the ₀-property are introduced and studied and the relation between them is investigated. Also, we show that, for ₀c ₀, these classes of spaces are in general different from the corresponding ones for ₀=c ₀, which have been extensively studied in the non-archimedean literature (see, for example, [1]–[6]).     

Functions related to convexity and smoothness of normed spaces

We introduce a few functions related to convexity and smoothness of normed spaces. Those functions turn out to be moduli of convexity or smoothness or play an intermediate role. We calculate the exact formulas for introduced functions in some classical Banach spaces. An application to geometry of normed spaces is also indicated.     

Grandes deviations des diffusions sur les espaces de besov-orlicz et application

Dans cet article nous demontrons le principe de grandes déviations de Freidlin et Wentzeii pour les diffusions suivant la topologie de l'espace de Besov-Orlicz. Nous étendons ainsi le résultat de Ben Arous et Ledoux [3] concernant le cas höldérien et celui de Roynetie [16] tiaitant le cas du mouvement brownien en norrne de Besov Comme application on établit la loi fonctionnelle du Logarithme itéré de Strassen pour l'aire de Lévy en norme de Besov-Orlicz. Cette loi est plus fine que celle obtenue par N'zi et Eddahbi [14] avec la norme Hölderienne

In this paper, we prove a Freidlin-Wentzell large deviations principle in Besov-Orlicz space for diffusion processes. Our result is an extension of that of Ben-Arous and Ledoux [3] who have treated the Hölder norm case and that of Roynette [16] who have considered Brownian motion in Besov space. As an application, we establish a Strassen's law of the iterated logarithm for Lévy's area process. This law is more sharper than the one in Hölder norm obtained by N'zi and Eddahbi [14]     

Restricted p-Centers for Sets in Real Locally Convex Spaces

ABSTRACT

Let p be a continuous seminorm on a real locally convex space X. The current paper is concerned with the problem of restricted p-centers in X. Characterizations of restricted p-centers and strongly unique restricted p-centers with respect to a “sun” are provided, and then some recent results due to Laurent and Pai [9 P. J. Laurent and D. Pai ( 1998 ). On simultaneous approximation . Numer. Funct. Anal. Optim. 19 : 1045 – 1064 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]] are extended and improved.     

On an extreme class of real interpolation spaces

We investigate the limit class of interpolation spaces that comes up by the choice θ=0 in the definition of the real method. These spaces arise naturally interpolating by the J-method associated to the unit square. Their duals coincide with the other extreme spaces obtained by the choice θ=1. We also study the behavior of compact operators under these two extreme interpolation methods. Moreover, we establish some interpolation formulae for function spaces and for spaces of operators.     

Radial rapid decay property for cocompact lattices

We study Haagerup inequality for radial functions on uniform lattices in semisimple Lie groups, with respect to Riemannian metrics and, in some case, to word metrics. In particular we extend the Swiatkowski-Valette results to any lattice acting properly and essentially transitively on classical buildings.     

Generalized Hyers-Ulam stability for general additive functional equations in quasi-β-normed spaces

In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. The first author of this paper investigated the Hyers-Ulam stability of Cauchy and Jensen type additive mappings. In this paper we generalize results obtained for Jensen type mappings and establish new theorems about the Hyers-Ulam stability for general additive functional equations in quasi-β-normed spaces.