Hilbert空间K-Fusion框架的构造

给出Hilbert空间中K-fusion框架的多种构造方法,包括利用一个K-fusion框架的合成算子去构造另一个K-fusion框架,利用两个fusion-Bessel序列及有界线性算子K去构造K-fusion框架.最后利用关于两个fusion-Bessel序列的有界线性算子S(VW)去构造新的K-fusion框架.     

K-框架和紧K-框架的算子扰动的稳定性

该文在Hilbert 空间中讨论K-框架和紧K-框架在算子扰动中的稳定性.首先给出K-框架经过有界线性算子T 扰动后为K-框架的充要条件,其次讨论了用两个Bessel 序列或者两个K-框架构造新的K-框架的方法,最后给出用两个Bessel 序列构造紧K-框架的充要条件.这些结果推广和改进了由Christensen和Ca...     

Hilbert空间中K-g-框架的一些新结果

利用算子理论方法构建了Hilbert空间中K-g-框架的一个新对偶,通过它等价刻画了关于不同闭子空间序列的K-g-框架和g-Bessel序列之间的关系.特别地,利用对偶K-g-框架得到了K-g框架稳定性的新结果.此外给出了构造K-g-框架的一些新方法.     

算子序列的升标和降标

本文研究了与算子紧序列有关的一类算子序列和算子上半Fredholm序列的升标和降标的一些性质.利用同伦的思想证明了具有有限升标(降标)的算子上半Fredholm序列在其摄动类中交换元的摄动下具有同样性质,从而把单个半Fredholm算子的有关结果推广到算子序列.     

一类非线性二元算子方程的迭代求解及其应用

运用锥与半序理论与混合单调算子理论,讨论半序Banach空间一类非线性二元算子方程解的存在唯一性,并给出迭代序列收敛于解的误差估计.作为应用,讨论了不具有单调性的算子方程的可解性,所得结果是某些已有结果的本质改进和推广.     

Hilbert空间中强半压缩算子迭代序列的误差估计及稳定性分析

在实Hilbert空间中,本文讨论强半压缩算子下的迭代序列的误差估计式和强收敛定理,并举例与已有迭代序列的误差估计式进行对比.进一步地,分析该迭代序列的稳定性.我们的结果推广了许多已知结论.     

一类非线性算子的带误差的Ishikawa迭代程序及其稳定性

建立了任意实Banach空间中带误差的Ishikawa迭代程序逼近Lipschitz强伪压缩算子的不动点的一般性定理,指出已被广泛广泛研究的Ishikawa迭代序列的稳定性问题仅是带误差的Ishikawa迭代程序的特例,作为直接的应用,用不同于通常的方法证得任意实Banach空间中的Ishikawa迭代序列关于Lipschitz强伪压缩算子是稳定的,这些推广或发展了近期许多相应的结果。     

Hilbert空间中的g-框架类展开式与g-Riesz-Fischer序列

本文考虑了Hilbert空间中一些g-框架类展开式以及g-Riesz-Fischer序列.首先讨论了Hilbert空间中一类算子序列,该类算子序列不必是g-Bessel序列.本文证明了在某些条件下g-框架类展开式存在并且这些展开式保持了通常意义下的能量最小性质.然后讨论了满足下g-框架条件的算子序列,这些算子序列不必满足上g-框架界,得到了Hilbert空间的子空间中的g-框架类展开式,并且给出了一个满足下g-框架条件的算子序列的一个刻画.最后讨论了Hilbert空间中的g-Riesz-Fischer序列,该类算子序列与满足下g-框架条件的算子序列紧密相关,得到了g-Riesz-Fischer序列的一些刻画.     

无穷维Hilbert空间上框架的算子与范数

在框架理论研究中,哪类可逆算子能使得某些框架性质保持不变这个问题是基本和重要的,本文在无穷维Hilbert空间上对下述两个问题进行研究.问题1:哪类可逆算子能使得框架算子保持不变;问题2:哪类可逆算子能使得框架范数只相差一列常数.本文从抽象的算子理论和具体的构造方法两方面对问题1给出解答.利用框架的相容算子的概念,当把问题2中的可逆算子集换成一类较小的算子集时,得到了问题2的回答.     

序列次可分解算子的不变子空间格

本文研究了序列次可分解算子的不变子空间问题,得到了一类序列次可分解算子具有丰富的不变子空间格的结果,精细地刻划了这类序列次可分解算子的不变子空间格.     

广义框架在框架算子作用下的一些性质

运用自伴算子的谱理论,讨论了Hilbert空间上的广义框架在框架算子作用下的一些性质.     

Hillbert空间中的广义框架扰动

研究了在一些扰动条件下Hilbert广义框架的稳定性，得到了一些结果，这些结果是OLE Christensen关于Hilbert框架经典结果的推广。     

Decomposition of Analysis Operators and Frame Ranges for Continuous Frames

In this article, the measure space associated with a continuous frame is supposed to be σ-finite and positive, and a frame range is the range of the analysis operator for a continuous frame. Gabardo and Han in 2003 asked whether two frame ranges can both be contained in another one. To solve this problem, we give two decompositions of analysis operators and frame ranges for continuous frames respectively, which essentially establish a relationship between continuous frames and Hilbert-Schmidt operator valued frames. As applications, it follows that only separable Hilbert space can have a continuous frame, that there exists a continuous frame of Riesz-type if and only if the associated measure space is purely atomic, and that the sum of two frame ranges is still a frame range when the sum is closed. Finally, we construct a counterexample which shows that the Gabardo-Han problem is not necessarily true in general.     

Hilbert空间的无穷维Compound算子方程

In this article, we consider compound matrices and compound operator equations in a Hilbert space. First, we recall some concepts and main results introduced by Muldowney and by Roger Temam. After that we establish the rule of compound matrices in a Hilbert space, and obtain the expression of solution to a compound operator equation by using the method of operator semigroup. Our brief results generalize the corresponding results in a finite space.     

A new class of operators and a description of adjoints of composition operators

Starting with a general formula, precise but difficult to use, for the adjoint of a composition operator on a functional Hilbert space, we compute an explicit formula on the classical Hardy Hilbert space for the adjoint of a composition operator with rational symbol. To provide a foundation for this formula, we study an extension to the definitions of composition, weighted composition, and Toeplitz operators to include symbols that are multiple-valued functions. These definitions can be made on any Banach space of analytic functions on a plane domain, but in this work, our attention is focused on the basic properties needed for the application to operators on the standard Hardy and Bergman Hilbert spaces on the unit disk.     

Frames for operators

Frames in Hilbert spaces are a redundant set of vectors which yield a representation for each vector in the space. In the present paper, we give a generalization of frames, which allows, in a stable way, to reconstruct elements from the range of a linear and bounded operator in a Hilbert space.     

Preservation of the Range under Perturbations of an Operator

A sufficient condition for the stability of the range of a positive operator in a Hilbert space is given. As a consequence, we get a class of additive perturbations which preserve regularity of the critical point of a positive operator in a Krein space.

     

The unique solution of the Karcher equation and the self-adjointness of the Karcher mean

Lawson and Lim showed that the Karcher equation for positive invertible operators on a Hilbert space has a unique solution using the method of the implicit function theorem of a Banach space. In this paper, in the framework of the operator inequality, we show the equivalence of the unique solution of the Karcher equation and the self-adjointness of the Karcher mean. For this, we reform the notion of the operator power means of negative order by virtue of the Tsallis relative operator entropy of negative order.     

Hilbert空间中的紧K-框架

K-框架是框架的一种推广.本文在Hilbert空间将紧框架推广到K-框架上,引入紧K-框架的概念.通过紧K-框架的算子K和合成算子给出紧K-框架的算子刻画,并利用紧K-框架的算子K给出紧K-框架成为紧框架的一个充要条件.还讨论紧K-框架的构造以及两个紧K-框架集的包含与涉及的算子K的相互关系.     

标准算子代数上的和导子有关的函数方程的Hyers-Ulam-Rassias稳定性

设■是复Hilbert空间,■是■上有界线性算子全体,■是标准算子代数且对于伴随运算封闭.本文结合广义Jensen等式证明了标准算子代数■上的和导子有关的函数方程具有广义Hyers-Ulam-Rassias稳定性.