Weak exactness for dual operator spaces

We introduce a new tensor product and study the weak^∗ condition C^′, which is also called weak^∗ exactness, for dual operator spaces. Our definition of weak^∗ condition C^′ is equivalent to Kirchberg's notion of weak exactness in the case of von Neumann algebras. We also study the connection of weak^∗ exact W^∗-TROs with their linking von Neumann algebras and study the structure of exact (respectively, nuclear) W^∗-TROs.     

A family of simple C1-algebras related to weighted shift operators

In this paper we study a family of C¹-algebras which occurs naturally in the study of C¹-algebras generated by weighted shifts. We show that these algebras are simple modulo the compacts, and while they share many of the properties of uniformly hyperfinite C¹-algebras, they are not approximately finite dimensional.     

JC代数的乘子代数

本文用双中心子刻画了JC代数的乘子代数,并且研究了复C^*-代数的自伴部分的乘子代数生成的C^*-代数与原C^*-代数的乘子代数之间的关系,最后研究了JB代数的扩张.     

Anderson Duality in K-Theory and Im(J)-Theory

We study Anderson duality for connective K-theory l and Im(J)-theory A, the latter being the p-localization of Quillen's algebraic K-theory of a suitably chosen finite field. The interplay between Anderson duality and Postnikov decomposition results in a construction of two families of natural transformations from ordinary cohomology theory to l^* and A^*-theory, which are related to the Chern character. These operations are then used to study l^*(l) and A^*(A), the cohomology operations of connective K-theory and Im(J)-theory.     

Standardness of *-representations of the algebra of smooth finite functions

We study strongly continuous *-representations by unbounded operators of the algebra of smooth finite functions on R^N. We establish that the closure of a strongly continuous *-representation of the algebraD(R^N), satisfying a certain condition, is self-adjoint and standard. We also study the correspondence between the strongly continuous *-representations ofD(R^N) and the continuous representations of the group R^N with respect to addition by symmetric operators.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 5, pp. 713–716, May, 1990.     

On*-primes and*-valuations

We study the relation between^*-primes and^*-valuations to deduce a necessary and sufficient condition for extending^*-valuations.     

"Anneaux noetheriens a droite entiers sur un sous-anneau de leur centre"

Let R be a ring and G a finite group of automorphisms of R such that GL^-1? R. In the first section, we study the homological and injective dimensions of R ^G when R is simple. In the second section, we suppose that R is a k-algebra and study c,the transfer of the Nullstellensatz property between R and R^G In the last section, we apply these results to envelopping atgebras of Lie algebras and Weyl algebras.     

Partially-bent functions

We study a conjecture stated in [6] about the numbers of non-zeros of, respectively, the auto-correlation function and the Walsh transform of the function (–1) ^f(x) , wheref(x) is any boolean function on {0, 1} ⁿ . The result that we obtain leads us to introduce the class of partially-bent functions. We study within these functions the propagation criterion. We characterize those partially-bent functions which are balanced and prove a relation between their number (which is unknown) and the number of non-balanced partially-bent functions on {0, 1} ^n–1. Eventually, we study their correlation immunity.     

Geometric and cohomological properties of rank 2 vector bundles on curves

Here we study the postulation of curves embedded in a smooth quadric hypersurface of P ⁴ and P ⁵ and relate this subject to the study of cohomological properties of rank 2 spanned vector bundles on smooth projective curves. Received: May 25, 2000; in final form: January 3, 2001?Published online: May 29, 2002     

On some congruence with application to exponential sums

We will study the solution of a congruence,x ≡g ^1/2)ωg(2 ⁿ ) mod 2 ⁿ , depending on the integersg andn, where ω _g (2 ⁿ ) denotes the order ofg modulo 2 ⁿ . Moreover, we introduce an application of the above result to the study of an estimation of exponential sums.     

Approximation by Nonlinear Multivariate Sampling Kantorovich Type Operators and Applications to Image Processing

In this article, we study a nonlinear version of the sampling Kantorovich type operators in a multivariate setting and we show applications to image processing. By means of the above operators, we are able to reconstruct continuous and uniformly continuous signals/images (functions). Moreover, we study the modular convergence of these operators in the setting of Orlicz spaces L ^?(? ⁿ ) that allows us to deal the case of not necessarily continuous signals/images. The convergence theorems in L ^p (? ⁿ )-spaces, L ^αlog ^β L(? ⁿ )-spaces and exponential spaces follow as particular cases. Several graphical representations, for the various examples and image processing applications are included.     

Properties of certain semigroups and their potential as platforms for cryptosystems

In this paper, we study some properties of semigroups with presentation 〈a,b ; a ^p =b ^r ,a ^q =b ^s 〉. We will also study their potential as platforms for the Diffie-Hellman key exchange protocol.     

Source-type solutions of degenerate diffusion equations with absorption

The object of this paper is to study the existence of a solution of the Cauchy problemu _t=Δu^m−u^p, u(x,0)=δ(x) and when a solution exists, to study its behaviour ast→0.     

Espaces Hp au dessus de l'espace hermitien hyperbolique de Cn (n > 1), II

Growth of harmonic functions and boundary values in a Sobolev space; comparison between the H^p space associated to Calderón Lusin's area integral and the H^p space associated to the maximal admissible function; study of Littlewood-Paley functions for the harmonic functions for the invariant laplacian of the hermitian hyperbolic space; relation between a Littlewood-Paley function and the bounded mean oscillation functions; study of H¹ and H¹ B.M.O. duality.     

The Riemannian <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> topology on the manifold of Riemannian metrics

We study the manifold of all Riemannian metrics over a closed, finite-dimensional manifold. In particular, we investigate the topology on the manifold of metrics induced by the distance function of the L ² Riemannian metric—so-called because it induces an L ² topology on each tangent space. It turns out that this topology on the tangent spaces gives rise to an L ¹-type topology on the manifold of metrics itself. We study this new topology and its completion, which agrees homeomorphically with the completion of the L ² metric. We also give a user-friendly criterion for convergence (with respect to the L ² metric) in the manifold of metrics.     

Multiplier operators and extremal functions related to the dual dunkl-sonine operator

We study the dual Dunkl-Sonine operator ^tS_k,? on ?^d, and give expression of ^tS_k,?, using Dunkl multiplier operators on ?^d. Next, we study the extremal functions f^*_λ, λ >0 related to the Dunkl multiplier operators, and more precisely show that {f^*_λ} λ >0 converges uniformly to ^tS_k,?(f) as λ → 0+. Certain examples based on Dunkl-heat and Dunkl-Poisson kernels are provided to illustrate the results.     

Homogenization of eigenvalue problem for Laplace–Beltrami operator on Riemannian manifold with complicated ‘bubble‐like’ microstructure

We study the asymptotic behavior of the eigenvalues and the eigenfunctions of the Laplace–Beltrami operator on a Riemannian manifold M^ε depending on a small parameter ε>0 and whose structure becomes complicated as ε→0. Under a few assumptions on scales of M^ε we obtain the homogenized eigenvalue problem. In addition we study the behavior of the heat equation on M^ε and investigate the large time behavior of the homogenized equation. Copyright © 2009 John Wiley & Sons, Ltd.     

L 2-Cohomology for Von Neumann Algebras

We study L ²-Betti numbers for von Neumann algebras, as defined by D. Shlyakhtenko and A. Connes in [CoS]. We give a definition of L ²-cohomology and show how the study of the first L ²-Betti number can be related to the study of derivations with values in a bi-module of affiliated operators. We show several results about the possibility of extending derivations from sub-algebras and about uniqueness of such extensions. In particular, we show that the first L ²-Betti number of a tracial von Neumann algebra coincides with the corresponding number for an arbitrary weakly dense sub-C*-algebra. Along the way, we prove some results about the dimension function of modules over rings of affiliated operators which are of independent interest. Received: March 2006 Revision: October 2006 Accepted: October 2006     

INTERPOLATION SPACES BETWEEN H^1 AND L^∞ ON SPACES OF HOMOGENEOUS TYPE

Using the maximal function characterization of Hardy spaces,we study the interpolation spaces between H^1 and L^∞on spaces of homogeneous type.