Perturbations of Invertible Operators and Stability of g-Frames in Hilbert Spaces

In this paper, we study the perturbations of invertible operators and stability of g-frames in Hilbert spaces. In particular, we obtain some conditions under which the perturbations of an invertible operator are still an invertible operator, the perturbations of a right invertible operator or a surjective operator are still a right invertible operator or surjective operator. Then we apply the perturbations of invertible operators to study the stability of g-frames which is close related with the invertibility (or right invertibility) property of operators.     

Some Unitary Operators on Hoop-algebras

In this paper, we introduce the notions of multiplier, $\odot$-closure operator and modal operator on hoop-algebras. After that, we investigate some algebraic properties of multiplier, $\odot$-closure operator and modal operator on hoop-algebras. Then we study relationships between multiplier and closure operator on hoop-algebras showing that, any monotone modal operator on hoop-algebra serves as a closure operator. Finally we represent image of hoop-algebra under the closure operator can be a hoop-algebra.     

一些蕴含Furuta不等式的算子单调函数的算子不等式

本文研究了算子不等式与算子单调函数之间的联系.利用关于算子单调函数的乘积引理,乘积定理等基本控制原理,给出许多算子不等式,这些不等式可包含正算子理论中应有十分广泛的Furuta不等式.     

Characterization of Riesz bases of wavelets generated from multiresolution analysis

We investigate Riesz bases of wavelets generated from multiresolution analysis. This investigation leads us to a study of refinement equations with masks being exponentially decaying sequences. In order to study such refinement equations we introduce the cascade operator and the transition operator. It turns out that the transition operator associated with an exponentially decaying mask is a compact operator on a certain Banach space of sequences. With the help of the spectral theory of the compact operator we are able to characterize the convergence of the cascade algorithm associated with an exponentially decaying mask in terms of the spectrum of the corresponding transition operator. As an application of this study we establish the main result of this paper which gives a complete characterization of all possible Riesz bases of compactly supported wavelets generated from multiresolution analysis. Several interesting examples are provided to illustrate the general theory.     

Applications of polar decompositions of idempotent and 2-nilpotent operators

An operator means a bounded linear operator on a complex Hilbert space. Using two polar decompositions of idempotent and 2-nilpotent operators, we shall study numerical radii of these two operators and finally we shall discuss two operator transformations, one of which is the generalized Aluthge transformation and another is an extension of the operator transformation by Patel-Tanahashi-Uchiyama.     

A representation theorem for local operator spaces

In this note, we generalize Ruan’s representation theorem and propose an Arveson-Hanh-Banach-Webster theorem for local operator spaces. Further, we investigate the decompos-ability of a complete contraction acting from a unital multinormed C*-algebra to a local operator System into a product of contractions and a unital contractive *-representation, and we study injectivity in both local operator space and local operator System contexts.     

Generalized weighted exponential proportional aggregation operators and their applications to group decision making

We present a new aggregation operator called the generalized ordered weighted exponential proportional averaging (GOWEPA) operator, which is based on an optimal model. We study some properties and different families of the GOWEPA operator. We also generalize the GOWEPA operator. The key advantage of the GOWEPA operator is that it is an aggregation operator with theoretic basis on aggregation. Moreover, we propose an orness measure of the GOWEPA operator and indicate some properties of this orness measure. Furthermore, we introduce the least exponential squares method (LESM) to determine the GOWEPA operator weights based on its orness measure. In the end, we develop an application of the new approach in a case of group decision making in investment selection.     

Generalized Fock spaces and Weyl relations for the Dunkl kernel on the real line

In this paper we study a class of generalized Fock spaces associated with the Dunkl operator. Next we introduce the commutator relations between the Dunkl operator and multiplication operator which leads to a generalized class of Weyl relations for the Dunkl kernel.     

Characterization of the QWN-conservation operator and applications

Based on the finding that the quantum white noise (QWN) conservation operator is a Wick derivation operator acting on white noise operators, we characterize the aforementioned operator by using an extended techniques of rotation invariance operators in a first place. In a second place, we use a new idea of commutation relations with respect to the QWN-derivatives. Eventually, we use the action on the number operator. As applications, we invest these results to study three types of Wick differential equations.     

Multidimensional Jensen’s operator on a Hilbert space and applications

Motivated by a joint concavity of connections, solidarities and multidimensional weighted geometric mean, in this paper we extend an idea of convexity (concavity) to operator functions of several variables. With the help of established definitions, we introduce the so called multidimensional Jensen’s operator and study its properties. In such a way we get the lower and upper bounds for the above mentioned operator, expressed in terms of non-weighted operator of the same type. As an application, we obtain both refinements and converses for operator variants of some well-known classical inequalities. In order to obtain the refinement of Jensen’s integral inequality, we also consider an integral analogue of Jensen’s operator for functions of one variable.     

Dimensions of the Kernels of linear operators and their algebraic adjoints

In this paper we study the kernels of a linear operator and its algebraic adjoint by studying their restriction on a subspace, a Banach space, such that the restriction is the difference of the identity and a compact operator under some conditions, and therefore some results on compact operator theory can be applied. As an example we study theM-scale subdivision operators.     

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 the Spectrum of the Reflection Operator on Conical Surfaces

We study the mapping properties of the reflection operator on a conical surface. This allows us to derive regularity results for the solution of the radiosity equation on conical surfaces in a scale of weighted Sobolev spaces. To motivate the calculations we first study the operator on a cylinder. Here we estimate the asymptotic behavior of the spectrum of the reflection operator by partial integration. This method works also for the conical case, but first we have to find a simple representation for some hypergeometric functions.     

一个双曲-椭圆耦合系统解的存在唯一性

本文研究了一个双曲-椭圆耦合系统.通过能量方法建立了有关微分算子的一些先验估计,构造了一个闭线性算子,证明了该闭线性算子为一个有界收缩线性算子半群的无穷小生成元.在此基础上,利用半群理论具体证明了双曲-椭圆耦合系统解的存在唯一性.     

具有扭转耦合效应的复合薄壁梁黎斯基的性质和指数稳定性(英文)

研究了具有扭转耦合效应的复合薄壁梁黎斯基的性质以及指数稳定性.首先证明该系统决定算子的预解式是紧的,且可生成群.其次,通过对该系统算子谱的渐近分析,证明了除至多有限个本征值外,其算子的谱是单重可分离的.特殊地,我们获得了自由系统的频率渐近表达式,因而利用克尔德什定理,证明了在希尔伯特状态空间中算子广义本征函数列的完备性.最后,结合黎斯基的性质及算子谱的分布证明了该系统的指数稳定性.     

一类人与出租车构成的排队模型主算子的谱特征

运用C0-半群理论研究一类人与出租车构成的排队模型主算子的谱特征.首先证明0是对应于该排队模型的主算子的几何重数为1的特征值,其次证明在虚轴上除了0以外其他所有点都属于该算子的豫解集,然后证明0是该主算子共轭算子的特征值.     

Doubly stochastic quadratic operators and Birkhoff’s problem

In the present we introduce a concept of doubly stochastic quadratic operator. We study necessary and sufficient conditions for doubly stochasticity of operator. Moreover, we study analogue of Birkhoff’s theorem for the class of doubly stochastic operators.     

扭的Heisenberg-Virasoro顶点算子代数的一个特征化（英文）

The twisted Heisenberg-Virasoro algebra is the universal central extension of the Lie algebra of differential operators on a circle of order at most one. In this paper, we first study the variety of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra, which is a finite set consisting of two nontrivial elements. Based on this property,we also show that the twisted Heisenberg-Virasoro vertex operator algebra is a tensor product of two vertex operator algebras. Moreover, associating to properties of semi-conformal vectors of the twisted Heisenberg-Virasoro vertex operator algebra, we charaterized twisted Heisenberg-Virasoro vertex operator algebras. This will be used to understand the classification problems of vertex operator algebras whose varieties of semi-conformal vectors are finite sets.     

On a class of quasi-Fredholm operators

We study a class of bounded linear operators acting on a Banach spaceX called B-Fredholm operators. Among other things we characterize a B-Fredholm operator as the direct sum of a nilpotent operator and a Fredholm operator and we prove a spectral mapping theorem for B-Fredholm operators.IMemory of my father, Sidi-Bouhouria 1914-0991.     

带有反馈与起动故障的M/G/1重新访问排队系统的适定性分析

文章研究一个带有贝努利反馈且系统服务台经常遭受启动故障的重新访问排队系统模型,利用线性算子半群理论,通过对描述其系统行为的偏微分方程组的研究,证明了该模型所描述的系统所确定的算子是闭稠定耗散算子,生成C0压缩半群,从而得到系统的适定性.在证明1是算子的预解点时,采用了共轭方法.