Applications of two-sided α-generalized derivations to 3-prime near rings

Let N be a zero symmetric 3-prime right near ring and α:N→N be an endomorphism. In this paper, the notions of two-sided α-(generalized) derivations on N are studied. Some results characterize commutativity of 3-prime near rings are obtained. Examples proving the necessity of the 3-primeness hypothesis are given. When α = id_N, one can easily obtain the main results of [5 Bell, H. E., Boua, A., Oukhtite, L. (2015). Semigroup ideals and commutativity in 3-prime near rings. Commun. Algebra 43:1757–1770.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]].     

Commutativity in special unitary groups at odd primes

It is a classical result by Bott that SU(s) and SU(t) homotopy commute in SU(n) if and only if s+t?n. We consider the p-localization analog of this problem and give an answer at odd primes.     

On products of unbounded operators

A symmetric operator X^ is attached to each operator X that leaves the domain of a given positive operator A invariant and makes the product AX symmetric. Some spectral properties of X^ are derived from those of X and, as a consequence, various conditions ensuring positivity of products of the form AX ₁ ... X _n are proved. The question of ^-complete positivity of the mapping p → Ap(X ₁,...,X _n) defined on complex polynomials in n variables is investigated. It is shown that the set ω is related to the McIntosh-Pryde joint spectrum of (X ₁,...,X _n) in case all the operators A, X ₁,...,X _n are bounded. Examples illustrating the theme of the paper are included. This revised version was published online in June 2006 with corrections to the Cover Date.     

标准算子代数上保因子交换性的映射

Let X, Y be real or complex Banach spaces with dimension greater than 2 and A, B be standard operator algebras on X and Y, respectively. Let φ ：A →B be a unital surjective map. In this paper, we characterize the map φ on .4 which satisfies （A - B）R = R（A-B） ξR （（A-B）→ （φ（B））φ（R） =φ（R）（（A）- （B）） for A, B, R E .4 and for some scalar     

Commutativity of rings with polynomial constraints

Let p, q and r be fixed non-negative integers. In this note, it is shown that if R is left (right) s-unital ring satisfying , respectively) where , then R is commutative. Moreover, commutativity of R is also obtained under different sets of constraints on integral exponents. Also, we provide some counterexamples which show that the hypotheses are not altogether superfluous. Thus, many well-known commutativity theorems become corollaries of our results.     

Curvature invariants, differential operators and local homogeneity

We first prove that a Riemannian manifold with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.

     

G-度量空间中两对非相容映象的几个新的公共不动点定理

在G-度量空间的框架下,利用自映象对的非相容性和(Ag)型R-弱交换性条件,在既不要求空间的完备性,也不要求映象连续的条件下,建立了一类?-压缩条件下的4个映象的几个新的公共不动点定理,此定理在很大程度上改进和发展了已有文献的相关结果.     

调和Dirichlet空间上Toeplitz算子与小Hankel算子的交换性

本文研究了调和Dirichlet空间上调和符号的Toeplitz算子与小Hankel算子交换性的问题.利用算子矩阵表示的方法,获得了调和Dirichlet空间上调和符号的Toeplitz算子与小Hankel算子交换的充要条件,将Dirichlet空间上的相应结果推广到了调和Dirichlet空间上.     

On Generalizations of Commutativity

This note is concerned with generalizations of commutativity. We introduce identity-symmetric and right near-commutative, and study basic structures of rings with such ring properties. It is shown that if R is an identity-symmetric ring, then the set of all nilpotent elements forms a commutative subring of R. Moreover, identity-symmetric regular rings are proved to be commutative. The near-commutativity is shown to be not left-right symmetric, and we study some conditions under which the near-commutativity is left-right symmetric. We also examine the near-commutativity of skew-trivial extensions, which has a role in this note.