正交射影在广义框架理论中的应用

本文研究了可分的Hilbert空间H中的广义框架,运用算子理论方法,研究了可分的 Hilbert空间H中广义框架的性质,给出了广义框架的对偶广义框架的一些刻画,并且证明了两个广义框架是强非交的一个充分必要条件．     

广义框架和广义Riesz基的摄动

引入并研究了Banach空间X中的Bessel集、广义框架与广义Riesz基．对X中的任一Bessel集{gm}m∈M，定义有界线性算子T：L^2（P）→X^＊，利用算子丁，给出了Bessel集与广义框架的等价刻画．同时讨论了广义框架和广义Riesz基的摄动．     

关于交半格同态构成的函数空间与FS-交连续Domain

定义了一类序结构—FS-交连续domain,讨论其相关性质并证明:(1)FS-交连续domain关于由Scott连续且保持非空有限交运算的函数构成的函数空间封闭,以(代数)FS-交连续domain为对象、以Scott连续函数为态射的范畴是Cartesian闭范畴;(2)任意分配可乘的有界完备domain是FS-交连续domain,从而紧连续dcpo的Smyth幂domain是FS-交连续domain.这些结果表明,FS-交连续domain是关于保非空有限交的连续映射构成的函数空间封闭的最恰当序结构.     

关于交半格同态构成的函数空间与FS-交连续Domain

定义了一类序结构-FS-交连续domain,讨论其相关性质并证明:(1)FS-交连续domain关于由Scott连续且保持非空有限交运算的函数构成的函数空间封闭,以(代数)FS-交连续domain为对象、以Scott连续函数为态射的范畴是Cartesian闭范畴;(2)任意分配可乘的有界完备domain是FS-交连续domain,从而紧连续dcpo的Smyth幂domain是FS-交连续domain.这些结果表明,FS-交连续domain是关于保非空有限交的连续映射构成的函数空间封闭的最恰当序结构.     

Hilbert空间H中带符号广义框架的一个刻画

本文研究了可分的Hilbert空间H中带符号广义框架,利用算子理论方法,给出了H中一族向量{hm}m∈M是一个带符号广义框架当且仅当带符号广义框架的框架算子的正部S 和负部S-是有界线性算子,讨论了H中带符号广义框架的框架算子S的可逆性,并且得到了H中每个向量f关于带符号广义框架{hm}m∈M和其对偶带符号广义框架{~hm}m∈M的表示式.     

Hilbert空间中的广义K-框架

通过引入广义K-框架和广义K-原子系统给出了Hilbert空间上有界线性算子K的值域的一种新的重构方式.广义K-框架是Hilbert空间中广义框架和K-框架概念的一种新的推广.为了建立基于广义K-框架的元素重构理论,广义K-对偶对和广义逼近K-对偶对的概念被引入.此外,广义K-框架和广义K-原子系统之间的关系,广义K-对偶对的存在条件以及广义K-对偶对和广义逼近K-对偶对之间的联系等问题被深入地讨论和研究.     

广义框架和框架算子

本文研究了可分的Hilbert空间H中的广义框架,应用算子论方法给出了广义框架是H中紧广义框架,对偶广义框架,独立广义框架的充要条件:证明了有关广义框架算子的一些结果。     

由规则交算子构造的具有泛逼近能力的模糊控制器的充分条件和必要条件

引进规则交算子的概念,并给出29个规则交算子;分别给出由规则交算子构造的模糊控制器具有泛逼近能力的充分条件和必要条件.     

Hilbert空间中的K-框架

K-框架是框架理论的一种推广.K-框架可以用于重构Hilbert空间中有界线性算子值域内的元素.本文首先研究了K-框架与框架理论的关系,得到了紧K-框架成为框架当且仅当有界线性算子K是满的,给出了有界线性算子K具有闭值域的K-框架的一个充要条件.并利用有界线性算子K和合成算子构造K-框架,讨论在一定扰动条件下K-框架的稳定性.     

广义框架和算子的伪逆

运用Hilbert空间H上线性算子的伪逆，得到了关于广义框架的框架算子和综合算子的伪逆之间的关系，同时还给出了任意f∈H关于不满足广义框架上界条件的向量族（hm)m∈M的表达式。     

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.     

On the Orthogonality of Frames and the Density and Connectivity of Wavelet Frames

We examine some recent results of Bownik on density and connectivity of the wavelet frames. We use orthogonality (strong disjointness) properties of frame and Bessel sequences, and also properties of Bessel multipliers (operators that map wavelet Bessel functions to wavelet Bessel functions). In addition we obtain an asymptotically tight approximation result for wavelet frames.     

Welch bounds for cross correlation of subspaces and generalizations

Lower bounds on the maximal cross correlation between vectors in a set were first given by Welch and then studied by several others. In this work, this is extended to obtaining lower bounds on the maximal cross correlation between subspaces of a given Hilbert space. Two different notions of cross correlation among spaces have been considered. The study of such bounds is done in terms of fusion frames, including generalized fusion frames. In addition, results on the expectation of the cross correlation among random vectors have been obtained.     

保不交算子值域的一些性质

研究了保不交算子值域的性质,建立了保不交算子值域为Riesz子空间的一个刻画;又讨论了主理想和主带在保不交算子作用后的象的性质,一些相关结果也得以讨论.     

Stability of g-frames

g-Frames are natural generalizations of frames which cover many other recent generalizations of frames, e.g., bounded quasi-projectors, frames of subspaces, outer frames, oblique frames, pseudo-frames and a class of time-frequency localization operators. Moreover, it is known that g-frames are equivalent to stable space splittings. In this paper, we study the stability of g-frames. We first present some properties for g-Bessel sequences. Then we prove that g-frames are stable under small perturbations. We also study the stability of dual g-frames.     

Disjointness in hypercyclicity

We introduce a notion of disjointness for finitely many hypercyclic operators acting on a common space, notion that is weaker than Furstenberg's disjointness of fluid flows. We provide a criterion to construct disjoint hypercyclic operators, that generalizes some well-known connections between the Hypercyclicity Criterion, hereditary hypercyclicity and topological mixing to the setting of disjointness in hypercyclicity. We provide examples of disjoint hypercyclic operators for powers of weighted shifts on a Hilbert space and for differentiation operators on the space of entire functions on the complex plane.     

$W^\ast$-模上的标准广义框架的和

In this paper, the sum of standard generalized flames of Hilbert W^＊-module is studied intensively by using operator-theoretic-methods, and some conditions are given to assure that the sum of two or more standard generalized frames is a standard generalized frame.     

Generalized random linear operators on a Hilbert space

In this paper, we are concerned with generalized random linear operators on a separable Hilbert space. Generalized random linear bounded operators, generalized random linear normal operators and generalized random linear self-adjoint operators are defined and investigated. The spectral theorems for generalized random linear normal operators and generalized random linear self-adjoint operators are obtained.     

Hilbert空间H中G-框架等式

框架已获得广泛的应用,g-框架是框架的推广.本文运用算子理论方法,根据Hilbert空间H中的g-框架和g-框架算子的性质,得到有关g-框架的几个等式,给出一些有意义的结果.