Additive Jordan isomorphisms of nest algebras on normed spaces

Let X be a real or complex Banach space. Let and be two nest algebras on X. Suppose that φ is an additive bijective mapping from onto such that φ(A²)=φ(A)² for every . Then φ is either a ring isomorphism or a ring anti-isomorphism. Moreover, if X is a real space or an infinite dimensional complex space, then there exists a continuous (conjugate) linear bijective mapping T such that either φ(A)=TAT⁻¹ for every or φ(A)=TA∗T−1 for every .     

On an asymptotic behavior of elements of order in irreducible representations of the classical algebraic groups with large enough highest weights

The behavior of the images of a fixed element of order in irreducible representations of a classical algebraic group in characteristic with highest weights large enough with respect to and this element is investigated. More precisely, let be a classical algebraic group of rank over an algebraically closed field of characteristic 2$">. Assume that an element of order is conjugate to that of an algebraic group of the same type and rank naturally embedded into . Next, an integer function on the set of dominant weights of and a constant that depend only upon , and a polynomial of degree one are defined. It is proved that the image of in the irreducible representation of with highest weight contains more than Jordan blocks of size if and are not too small and .

     

On the ε-entropy of classes of holomorphic functions

Suppose thatB _R ^d is a ball of radiusR in ℂ ^d and σ is the standard measure on the unit sphere in ℂ ^d . ForR>1, 1≤p≤∞, and for the natural numbersl, d, byH _R ⁰ (l, p, d) we denote the class of functionsf holomorphic inB _R ^d and such that in the homogeneous polynomial expansion of the firstl summands the zero and radial derivatives of orderl belong to the closed unit ball of the Hardy spaceH ^p (B _R ^d ). In this paper an asymptotic formula for the ε-entropy of the classH _R ⁰ (l, p, d) in the spacesL ^p (σ), 1≤p<∞, and is obtained. Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 286–293, August, 2000.     

Novikov-Poisson algebras and associative commutative derivation algebras

We describe Novikov-Poisson algebras in which a Novikov algebra is not simple while its corresponding associative commutative derivation algebra is differentially simple. In particular, it is proved that a Novikov algebra is simple over a field of characteristic not 2 iff its associative commutative derivation algebra is differentially simple. The relationship is established between Novikov-Poisson algebras and Jordan superalgebras. Supported by RFBR (grant No. 05-01-00230), by SB RAS (Integration project No. 1.9), and by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (project NSh-344.2008.1). __________ Translated from Algebra i Logika, Vol. 47, No. 2, pp. 186–202, March–April, 2008.     

Multiple Eigenvalues in Spectral Analysis for Solving QBD Processes

A number of authors have recently suggested solving quasi birth-and-death (QBD) processes through the use of eigenvalue-based methods. These methods take on a special form when there are multiple eigenvalues present. We investigate this problem in a general setting as well as in the context of a specific preemptive priority queueing model.      

套代数上高阶导子的刻画

设N是Banach空间X上的套,AlgN是相应的套代数。本文证明了,若套N中存在一个非平凡元在X中可补,那么AlgN上的每个可加Jordan高阶导子和每个可加三重Jordan高阶导子都是高阶导子。     

基于系统空间结构的约当规范形广义特征向量的求解方法

基于系统空间结构的分析 ,给出了求解系统约当规范形广义特征向量的新方法 .与 [1 ]中给出的方法相比 ,本文的方法更简单直接 .最后举例说明了方法的应用 .     

Pseudo-atoms, atoms and a Jordan type decomposition in effect algebras

The aim of this paper is to introduce and investigate the concept of pseudo-atoms of a real-valued function m defined on an effect algebra L; a few examples of pseudo-atoms and atoms are given in the context of null-additive, null-null-additive and pseudo-null-additive functions and also, some fundamental results for pseudo-atoms under the assumption of null-null-additivity are established. The notions of total variation |m|, positive variation m⁺ and negative variation m⁻ of a real-valued function m on L are studied elaborately and it is proved for a modular measure m (which is of bounded total variation) defined on a D-lattice L that, m is pseudo-atomic (or atomic) if and only if its total variation |m| is pseudo-atomic (or atomic). Finally, a Jordan type decomposition theorem for an extended real-valued function m of bounded total variation defined on an effect algebra L is proved and some properties on decomposed parts of m such as continuity from below, pseudo-atomicity (or atomicity) and being measure, are discussed. A characterization for the function m to be of bounded total variation is established here and used in proving above-mentioned Jordan type decomposition theorem.     

广义可加Fuzzy测度

本文首先引入Fuzzy集类上（广义）可加Fuzzy测度的有关概念，然后给出Fuzzy集上关于可加Fuzzy测度的Fuaay积分及有关定理，最后在一定条件下给出广义可加Fuzzy测度的一系列分解定理。     

交换环上上三角矩阵代数在全矩阵代数中的扩代数及其若当导子

设R是任意含么交换环,2是R的可逆元.M(n,R)表示R上所有n×n级矩阵形成的代数,T(n,R)表示R上所有n×n级上三角矩阵形成的代数.决定了T(n,R)在M(n,R)中的扩代数,并具体刻画了这些扩代数的若当导子.