Weak convergence theorem for Lipschizian pseudocontraction semigroups in Banach spaces

The purpose of this paper is to study the weak convergence problems of the irnplicity iteration process for Lipschitzian pseudocontraction semigroups in general Banach spaces. The results presented in this paper extend and improve the corresponding results of Zhou [Nonlinear Anal., 68, 2977-2983 （2008）], Chen, et ah [J. Math. Anal. Appl., 314, 701 709 （2006）], Xu and Ori [Numer. Funct. Anal. Optim, 22, 767-773 （2001）] and Osilike [J. Math. Anal. Appl., 294, 73-81 （2004）]. Keywords     

广义算子半群与广义分布参数系统的适定性

首先,针对广义分布参数系统的求解问题,提出了由Hilbert空间中有界线性算子所引导的广义算子半群和广义积分半群;其次,讨论了广义预解算子的性质、广义算子半群与广义积分半群的性质;最后,研究了广义分布参数系统的适定性问题.     

Good B-quasi-Ehresmann semigroups

A semigroup S with a sub-band B is called a good B-quasi-Ehresmann semigroup if it is a Bsemiabundant semigroup satisfying the congruence condition such that B((ab)+)abB((ab)*)aB(a*)B(b+)b for all a,b ∈S.We show that every good B-quasi-Ehresmann semigroup has a global representation and a standard representation.As a special case,the structure of good quasi-adequate semigroups is described.     

关于序半群理想的根

Let S be an ordered semigroup.In this paper,we characterize ordered semigroups in which the radical of every ideal（right ideal,bi-ideal） is an ordered subsemigroup（resp.,ideal,right ideal,left ideal,bi-ideal,interior ideal） by using some binary relations on S.     

三角矩阵代数的自同构

本文研究了三角代数的自同构.利用三角代数的基本概念及自同构定义,得到三角代数的自同构形式,并刻画了其内自同构的具体形式.     

On the images of Sobolev spaces under the heat kernel transform on the Heisenberg group

The aim of this paper is to obtain certain characterizations for the image of a Sobolev space on the Heisenberg group under the heat kernel transform. We give three types of characterizations for the image of a Sobolev space of positive order $H^m(\mathbb {H}^n), m\in \mathbb {N}^n,$ under the heat kernel transform on $\mathbb {H}^n,$ using direct sum and direct integral of Bergmann spaces and certain unitary representations of $\mathbb {H}^n$ which can be realized on the Hilbert space of Hilbert‐Schmidt operators on $L^2(\mathbb {R}^n).$ We also show that the image of Sobolev space of negative order $H^{-s}(\mathbb {H}^n), s(>0) \in \mathbb {R}$ is a direct sum of two weighted Bergman spaces. Finally, we try to obtain some pointwise estimates for the functions in the image of Schwartz class on $\mathbb {H}^n$ under the heat kernel transform.     

On Adequate Transversals

We consider adequate transversals of abundant semigroups and prove that, in a particular case, there is a natural embedding of an inverse transversal within a certain regular subsemigroup. We also introduce the concepts of simplistic, perfect, and quasi-adequate transversal and provide a number of interesting connections between these.