Algebra matrix and similarity classification of operators

In this paper, by the Gelfand representation theory and the Silov idempotents theorem, we first obtain a central decomposition theorem related to a unital semi-simple n-homogeneous Banach algebra, and then give a similarity classification of two strongly irreducible Cowen-Douglas operators using this theorem.     

关于循环阵列码

本文用代数观点来研究循环阵列码,证明了一般的阵列码是一些极小循环阵列码的直和,并且对极小循环阵列码给出了明确的刻画．当有限域的特征不整除群的阶时,给出了直接写出相应的多项式环的本原幂等元的方法,从而可以直接写出所有的极小循环码．     

Commuting traces of multilinear maps on invertible elements

Let R be a unital simple ring. Under some technical restrictions, we characterize m-linear mappings G:R^m→R satisfying [G(u,…,u),u]?=?0 for all unit u∈R.     

A proof of W. T. Gowers' theorem

W. T. Gowers' theorem asserts that for every Lipschitz function and 0$">, there exists an infinite-dimensional subspace of such that the oscillation of on is at most . The proof of this theorem has been reduced by W. T. Gowers to the proof of a new Ramsey type theorem. Our aim is to present a proof of the last result.

     

ON THE INVERTIBILITY OF HILBERT SPACE IDEMPOTENTS

This note is to present some results on the group invertibility of linear combina- tions of idempotents when the difference of two idempotents is group invertible.     

关于N（2，2，0）代数的中间幂等元

为了深入研究N（2,2,0）代数的代数结构,在N（2,2,0）代数中建立了中间幂等元的概念,讨论了它的基本性质,给出了中间幂等元关联的集合坞是（S,＊,△,0）的子代数的一个条件．证明了当U（2,2,0）代数中包含一个右零半群时,Mg是幂等元集E（S）的子集．并利用坞定义了一个等价关系．     

Principally Quasi-Baer Skew Power Series Rings

Let α be an endomorphism of R which is not assumed to be surjective and R be α-compatible. It is shown that the skew power series ring R[[x; α]] is right p.q.-Baer if and only if the skew Laurent series ring R[[x, x ^?1; α]] is right p.q.-Baer if and only if R is right p.q.-Baer and every countable subset of right semicentral idempotents has a generalized countable join. Examples to illustrate and delimit the theory are provided.     

Additive Set of Idempotents in Rings

Let R be a ring with identity 1, I(R) be the set of all nonunit idempotents in R, and M(R) be the set of all primitive idempotents and 0 of R. We say that I(R) is additive if for all e, f ∈ I(R) (e ≠ f), e + f ∈ I(R), and M(R) is additive in I(R) if for all e, f ∈ M(R)(e ≠ f), e + f ∈ I(R). In this article, the following points are shown: (1) I(R) is additive if and only if I(R) is multiplicative and the characteristic of R is 2; M(R) is additive in I(R) if and only if M(R) is orthogonal. If 0 ≠ ef ∈ I(R) for some e ∈ M(R) and f ∈ I(R), then ef ∈ M(R), (2) If R has a complete set of primitive idempotents, then R is a finite product of connected rings if and only if I(R) is multiplicative if and only if M(R) is additive in I(R).