共查询到19条相似文献,搜索用时 46 毫秒
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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. 相似文献
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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). 相似文献
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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. 相似文献
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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. 相似文献
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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. 相似文献
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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. 相似文献
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George A. Elliott Katsunori Kawamura 《Transactions of the American Mathematical Society》2008,360(9):4841-4862
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.
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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. 相似文献
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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. 相似文献
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张伦传 《应用泛函分析学报》2003,5(3):210-212
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。 相似文献
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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. 相似文献
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