Matrices which commute with doubly stochastic matrices

The set doubly stochastic matrices which commute with the doubly stochastic matrices of any particular given rank is determined.     

Matrices which commute with doubly stochastic matrices

The set doubly stochastic matrices which commute with the doubly stochastic matrices of any particular given rank is determined.     

A note on compact graphs

An undirected simple graph G is called compact iff its adjacency matrix A is such that the polytope S(A) of doubly stochastic matrices X which commute with A has integral-valued extremal points only. We show that the isomorphism problem for compact graphs is polynomial. Furthermore, we prove that if a graph G is compact, then a certain naive polynomial heuristic applied to G and any partner G′ decides correctly whether G and G′ are isomorphic or not. In the last section we discuss some compactness preserving operations on graphs.     

Quantum integrability of Beltrami-Laplace operator as geodesic equivalence

Given two Riemannian metrics on a closed connected manifold , we construct self-adjoint differential operators such that if the metrics have the same geodesics then the operators commute with the Beltrami-Laplace operator of the first metric and pairwise commute. If the operators commute and if they are linearly independent, then the metrics have the same geodesics. Received: 11 February 2000; in final form: 20 August 2000/ Published online: 17 May 2001     

多圆盘上的本质可换的Toeplitz算子

本文讨论多圆盘上Ｂｅｒｇｍａｎ空间上的具有多重调和符号的Ｔｏｅｐｌｉｔｚ算子的本质可换性与可换性．我们获得了一个解析或共轭解析Ｔｏｅｐｌｉｔｚ算子与具有多重调和符号的Ｔｏｅｐｌｉｔｚ算子本质可换的充分必要条件是它们是可换的．     

重调和Hardy空间上的Toeplitz 算子

与调和Bergman 空间相对应, 本文研究重调和Hardy 空间h²(D²) 上的Toeplitz 算子. 本文发现, h²(D²) 上的Toeplitz 算子与经典的Hardy 空间、Bergman 空间及调和Bergman 空间上的Toeplitz算子的性质都有很大的差异. 例如解析Toeplitz 算子可以不是半可换及可交换的. 即使半可换, 其中任何一个符号可以不为常数; 即使可交换, 两个符号的非平凡线性组合也不一定是常数. 本文得到了h²(D²) 上两个解析Toeplitz 算子半可换和可换的充分必要条件.     

On a Problem of M. Kambites Regarding Abundant Semigroups

A semigroup is regular if it contains at least one idempotent in each ?-class and in each ?-class. A regular semigroup is inverse if it satisfies either of the following equivalent conditions: (i) there is a unique idempotent in each ?-class and in each ?-class, or (ii) the idempotents commute. Analogously, a semigroup is abundant if it contains at least one idempotent in each ?*-class and in each ?*-class. An abundant semigroup is adequate if its idempotents commute. In adequate semigroups, there is a unique idempotent in each ?* and ?*-class. M. Kambites raised the question of the converse: in a finite abundant semigroup such that there is a unique idempotent in each ?* and ?*-class, must the idempotents commute? In this note, we provide a negative answer to this question.     

多圆柱上Dirichlet空间中Toeplitz算子的交换性

本文讨论了多圆柱上Dirichlet空间中的正规Toeplitz算子以及全纯指标和反全纯指标的两个Toeplitz算子的交换性.我们证明具有多圆柱上Dirichlet空间中反全纯指标的两个Toeplitz算子可交换当且仅当两个指标是线性相关的,同时证明全纯指标和反全纯指标的两个Toeplitz算子可交换当且仅当两个指标有一个是常数.     

A note on the commutativity of groups

In this article, we show that a group is abelian if and only if every two elements of the same order commute.     

Commutants of analytic Toeplitz operators on the Bergman space

In this note we show that if two Toeplitz operators on a Bergman space commute and the symbol of one of them is analytic and nonconstant, then the other one is also analytic.