Hilbert C~*-模中g-框架的一些性质

本文运用算子理论方法,给出Hilbert C~*-模中g-框架的一些性质并讨论g-框架的扰动性,得到g-框架的和的一些刻画,所得结果推广和改进了已有的结果.     

Hilbert C~*-模上的广义g-框架

本文主要研究了Hilbert C~*-模上广义g-框架.给出了Hilbert C~*-模上的广义g-框架,广义g-框架算子,广义典则对偶g-框架及广义交错对偶g-框架的定义,并证明了有关广义g-框架的一些结果.     

多重C~*-动力系统在Hilbert C~*-模上的膨胀

研究了多重C~*-动力系统在Hilbert C~*-模上表示的膨胀.设(A,α)是一个多重C~*-动力系统,(π,T,E)是(A,α)的行压缩协变表示,证明了存在(π,T,E)的等距膨胀(ρ,V,F).     

Hilbert W*-模上的广义框架

本文研究了Hilbert W*-模上的广义框架.运用了算子理论的方法,得出了Hilbert W*-模上的广义框架的一些结果,与标准离散Hilbert C*-模框架的一些结果是相似的.     

Hilbert C*-模上框架(强)可补的充要条件

Hilbert C*-模上框架的框架变换的实质是将该模进行膨胀,使得该框架变换的值域存在标准正交基,以便于Hilbert C*-模上不同框架之间关系的研究.受此启发,本文引入了Hilbert C*-模上框架(强)可补的概念,给出并证明了Hilbert C*-模上有限个框架(强)可补的充要条件.     

准Hilbert C~*-模中Dunkl-Williams不等式的推广

给出了准Hilbert C~*_- 模中Dunkl-Williams不等式的进一步推广及其倒换,并刻画其等号成立的条件.     

Hilbert C*模上的Gabor酉系统

本文引入了Hilbert C*-模上的Gabor酉系统的概念,研究了它的基本性质,证明了膨胀定理,并给出某个酉系统的两个正规框架向量不相交的等价条件.     

Hilbert W*-模上的广义框架

本文给出了Hilbert W*-模上的标准广义框架的不相交,强不相交,弱不相交的定义,还给出了Hilbert W*-模上的广义框架的不相交,强不相交,弱不相交成立的条件,并且用算子理论的方法研究了它们的性质.     

有限模框架

研究有限生成Hilbert C*-模中的模框架,来源于信息论中的数据包编码理论.我们计算出模框架的势,刻画了在框架向量丢失的情况下模框架的稳健性和最框优架,得到了由一个或两个酉算子生成的酉系统的Parseval模框架向量的特征.     

Hilbert C~*-模中K-Fusion框架的刻画

首先通过权重集的选取改进了HilbertC~*-模中fusion框架的原有定义.然后将K-fusion框架的概念由Hilbert空间推广到Hilbert C~*-模中,并且利用算子理论方法得到了Hilbert C~*-模中K-fusion框架的一些等价刻画.     

A Hilbert bundle characterization of Hilbert C*-modules

The category of Hilbert C*-modules over a given C*-algebra is shown to be equivalent to a certain simply described category of Hilbert bundles (i.e., continuous fields of Hilbert spaces) over the space of pure states of the C*-algebra with the zero functional adjoined.

     

Bessel-type inequalities in Hilbert C *-modules

Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombieri and Boas–Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert C *-modules.     

Geometrical Aspects of Hilbert C*-modules

The aim of the present paper is to solve some major open problems of Hilbert C^*-module theory by applying various aspects of multiplier C^*-theory. The key result is the equivalence established between positive invertible quasi-multipliers of the C^*-algebra of compact operators on a Hilbert C^*-module {, ., } and A-valued inner products on , inducing an equivalent norm to the given one. The problem of unitary isomorphism of C^*-valued inner products on a Hilbert C^*-module is considered and new criteria are formulated. Countably generated Hilbert C^*-modules turn out to be unitarily isomorphic if they are isomorphic as Banach C^*-modules. The property of bounded module operators on Hilbert C^*-modules of being compact and/or adjointable is unambiguously connected to operators with respect to any choice of the C^*-valued inner product on a fixed Hilbert C^*-module if every bounded module operator possesses an adjoint operator on the module. Every bounded module operator on a given full Hilbert C^*-module turns out to be adjointable if the Hilbert C^*-module is orthogonally complementary. Moreover, if the unit ball of the Hilbert C^*-module is complete with respect to a certain locally convex topology, then these two properties are shown to be equivalent to self-duality.     

Hilben C*-模之间的同构定理

获得了Hilbert C^*-模之间的两个同构定理．作为推论，证明了C^*-代数上每个可数生成的Hilbert C^*-模均稳定酉等价于A。     

Generalizations of Bohr's inequality in Hilbert C*-modules

We present a new operator equality in the framework of Hilbert C*-modules. As a consequence, we get an extension of the Euler–Lagrange type identity in the setting of Hilbert bundles as well as several generalized operator Bohr's inequalities due to O. Hirzallah, W.-S. Cheung, J.E. Pe?ari? and F. Zhang.     

可补Hilbert C*-模及其有界模映射

给出了可补Hilbert C^*-模一系列等价刻画，获得了一类有界模映射的分解定理。