半环上矩阵的秩和坡上矩阵可逆的条件

研究了交换半环上矩阵的秩和坡上矩阵的可逆条件.利用Beasley的引理以及不变式,获得了交换半环上正则矩阵的行秩、列秩与Schein秩三者相等,以及坡上矩阵可逆的充要条件.推广模糊代数和分配格上矩阵的结果.     

半模的张量积

本文引入了半模的张量积的泛性定义，给出了半模范畴中的有向正向系的上极限以及任意一个半模同态的上核，讨论了半模张量积的若干性质，主要结果是：证明了张量函子保持半模的右正合性和上积，并且上积保持半模的平坦性，半模范畴中的张量函子保持上极限和上核．     

单位球上Hardy空间上的复合算子的本性模

利用导出映照的拉回测度和上极限,给出了单位球上Hardy空间上的复合算子的本性模的表示.     

分配格上上标准特征向量的求法

本文研究了分配格(L,∧,∨,0,1)上方阵A的上特征向量的性质.利用矩阵的伴随有向图,得到格上方阵A的上标准特征向量的一种实用的新方法.     

紧L-X半群上不同分布的组合乘积的极限性质

本文讨论一类紧拓扑半群上不同分布概率测度组合乘积的极限性质,利用“局部群化”的方法将紧群上,紧交换半群上的一些结果以相应的形式建立到紧L-X半群上.     

完全分配格上的覆盖粗糙集模型

将集合论中的覆盖概念抽象到完全分配格L上,利用它定义格L上关于覆盖的上(下)近似算子,给出格L上覆盖粗糙集模型.文中先讨论格L上覆盖的相关性质,进而研究了覆盖上(下)近似算子的性质,得到若干结果.     

从上半平面Hardy空间到增长型空间和Bloch空间上的加权复合算子的有界性

研究了从上半平面的Hardy空间到增长型空间和Bloch空间上的加权复合算子有界性的充要条件,给出了上半平面增长型空间上的加权复合算子有界性的充要条件,利用上半平面增长型空间和圆盘增长型空间之间的同构,获得了圆盘增长型空间上的加权复合算子有界性的充要条件.     

主理想整环上的线性方程组的通解

将文[1]中整数环上的线性方程组问题推广到主理想整环上,利用主理想整环上的矩阵的初等变换及等价标准形导出了主理想整环上的线性方程组有解的一个充分必要条件和求解方法.最后,通过实例说明了算法.     

分子格上伪补的构造

本文给出了分子格上伪补的构造定理，并证明了当一个非平凡分子格上有伪补，其既约因子上并不一定存在伪补，但其准既约因子上一定存在伪补，且任一分子格上的伪补都可表为其准既约因子上伪补的直积．     

一般集合上的两个函数和的图像的盒维数估计

本文研究了R1的非连通紧子集上的两个连续函数和的图像的盒维数估计的问题.利用构造反例的方法得到了与已有的结果完全不同的结论.通过引入适当的参量,进一步研究了Rn的非空有界子集上的两个函数和的图像的上、下盒维数估计,得到了其上、下界,并且构造了例子说明所得的上、下界能够达到.     

Weighted norm inequalities for the maximal commutators of singular integral operators

The maximal operator associated with the commutator of Calderón-Zygmund operator is considered. It is shown that the maximal commutator enjoys some two-weight norm estimates which are similar to those of the commutator of Calderón-Zygmund operator.     

Commutator length of symplectomorphisms

Each element $x$ of the commutator subgroup $[G, G]$ of a group $G$ can be represented as a product of commutators. The minimal number of factors in such a product is called the commutator length of $x$. The commutator length of $G$ is defined as the supremum of commutator lengths of elements of $[G, G]$. We show that for certain closed symplectic manifolds $(M,\omega)$, including complex projective spaces and Grassmannians, the universal cover $\widetilde{\hbox{\rm Ham}\, (M,\omega)$ of the group of Hamiltonian symplectomorphisms of $(M,\omega)$ has infinite commutator length. In particular, we present explicit examples of elements in $\widetilde{\hbox{\rm Ham}\, (M,\omega)$ that have arbitrarily large commutator length -- the estimate on their commutator length depends on the multiplicative structure of the quantum cohomology of $(M,\omega)$. By a different method we also show that in the case $c_1 (M) = 0$ the group $\widetilde{\hbox{\rm Ham}\, (M,\omega)$ and the universal cover ${\widetilde{\Symp}}_0\, (M,\omega)$ of the identity component of the group of symplectomorphisms of $(M,\omega)$ have infinite commutator length.     

Commutator subgroup of Vershik–Kerov group

We describe a commutator subgroup of Vershik–Kerov group over an infinite field and find the bound for its commutator width. This gives a partial solution of the problem posed by Sushchanskii in 2010. We also describe the lower central series of the group of infinite upper triangular matrices over an infinite field and find the bound for its commutator width.     

On upper bounds on stable commutator lengths in mapping class groups

We give new upper bounds on the stable commutator lengths of Dehn twists in mapping class groups and new lower bounds on the stable commutator lengths of Dehn twists in hyperelliptic mapping class groups. In particular, we show that the stable commutator lengths of Dehn twists about a nonseparating and a separating curve on an oriented closed surface of genus 2 are not equal to each other.     

Schechter Methods of Interpolation and Commutators

We study the relationship between Schechter's methods of complex interpolation and the so called commutator estimates. We obtain new commutator theorems and prove characterizations of the Domain and Range spaces associated with the corresponding quasilogarithmic operator. Our methods also provide a new approach to known results, including the higher order commutator theorems for the complex method recently obtained by R. Rochberg .     

非自伴算子代数的换位子

设T是复数域上的代数,T的换位子[T,T]指{[a,b]:a,6∈T}的线性扩张．本文给出了Nest代数T(N)的换位子[T(N),T(N)1]的σ-弱算子拓扑闭包的刻画,和TAF代数T的换位子[T,T]的范数闭包的几种刻画,进一步得到是T的理想．     

A Decomposition Formula for the Weighted Commutator

We decompose the weighted subobject commutator of M. Gran, G. Janelidze and A. Ursini as a join of a binary and a ternary commutator.     

A commutator approach to absolute continuity for unbounded Jacobi operators

This paper uses commutator equations to study the absolute continuity of spectral measures associated with certain subclasses of unbounded self-adjoint Jacobi matrix operators determined by properties of the diagonal and subdiagonal sequences. If the diagonal sequence is the zero sequence, properties of the difference sequence of the subdiagonal determine the choice of a bounded operator for the commutator equation. The structure of the resulting commutator leads to results on absolute continuity.     

Spectral radius inequalities for positive commutators

We establish several inequalities for the spectral radius of a positive commutator of positive operators in a Banach space ordered by a normal and generating cone. The main purpose of this paper is to show that in order to prove the quasi-nilpotency of the commutator we do not have to impose any compactness condition on the operators under consideration. In this way we give a partial answer to the open problem posed in the paper by J. Bra?i?, R. Drnov?ek, Y. B. Farforovskaya, E. L. Rabkin, J. Zemánek (2010). Inequalities involving an arbitrary commutator and a generalized commutator are also discussed.     

Stacky abelianization of algebraic groups

We prove a conjecture of Drinfeld regarding restriction of central extensions of an algebraic group G to the commutator subgroup. As an application, we construct the “true commutator” of G. The quotient of G by the action of the true commutator is the universal commutative group stack to which G maps.