共查询到19条相似文献,搜索用时 92 毫秒
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关于算子迹的Bellman不等式 总被引:3,自引:0,他引:3
周其生 《数学的实践与认识》2001,31(6):716-718
本文将矩阵中关于半正定 Hermite矩阵的 Bellman不等tr(AB) k tr(Ak Bk) ,k =1 ,2 ,…推广到 Hilbert空间 ,得到关于正的迹算子的相应不等式 相似文献
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关于矩阵和算子迹的一组不等式 总被引:1,自引:1,他引:0
周其生 《数学的实践与认识》2006,36(3):252-256
给出关于半正定矩阵迹和正算子迹的一组不等式,得到与邱贤忠关于实数的不等式的类似结果. 相似文献
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从矩阵迹关系过渡到算子迹关系的一个通用方法(Ⅱ) 总被引:6,自引:1,他引:5
周其生等人(1997年)给出了一个把半正定Hermite阵的迹关系推广到正迹类算子的相应关系的通用方法。本文把上述通用方法推广到Schatten类算子,并用它得到一些重要的算子迹不等式。 相似文献
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文[1]对Bellmen矩阵迹不等式做了进一步改进和推广,但征明需很多予备知识。本文用排序原理给出另一种简单的证明,并再给出一个新的矩阵迹的不等式,以供参考。 相似文献
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关于矩阵迹的平均不等式 总被引:2,自引:0,他引:2
关于矩阵迹的平均不等式黄礼平(湘潭矿业学院基础课部411201)近年来,对矩阵迹的不等式研究活跃,本文给出两个矩阵迹的平均不等式.定理1设A,B,C均为n阶半正定Hermite矩阵,则特别,我们有推论1设A,B,C均为n阶正定实对称矩阵,则诸等号当且... 相似文献
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A. Taghavi V. Darvish H. M. Nazari S. S. Dragomir 《Annali dell'Universita di Ferrara》2017,63(2):377-389
In this paper, we prove some singular value inequalities for sum and product of operators. Also, we obtain several generalizations of recent inequalities. Moreover, as applications we establish some unitarily invariant norm and trace inequalities for operators which provide refinements of previous results. 相似文献
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Ömer E?ecio?lu 《Journal of Combinatorial Theory, Series A》2010,117(1):77-103
In a recent paper we have presented a method to evaluate certain Hankel determinants as almost products; i.e. as a sum of a small number of products. The technique to find the explicit form of the almost product relies on differential-convolution equations and trace calculations. In the trace calculations a number of intermediate nonlinear terms involving determinants occur, but only to cancel out in the end.In this paper, we introduce a class of multilinear operators γ acting on tuples of matrices as an alternative to the trace method. These operators do not produce extraneous nonlinear terms, and can be combined easily with differentiation.The paper is self contained. An example of an almost product evaluation using γ-operators is worked out in detail and tables of the γ-operator values on various forms of matrices are provided. We also present an explicit evaluation of a new class of Hankel determinants and conjectures. 相似文献
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Mohamed Boumazgour 《Journal of Mathematical Analysis and Applications》2008,342(1):386-393
We use certain norm inequalities for 2×2 operator matrices to establish norm inequalities for sums of two basic elementary operators on a Hilbert space. Further, we give necessary and sufficient conditions under which the norm of the above sum of elementary operators attains its optimal value. Applications of the inequalities obtained are also considered. 相似文献
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设m是具有忠实正规半有限迹τ的Hilbert空间上的一个半有限von Neumann代数.隶属于m的—个闭稠定算子x称为τ可测,如果存在常数λ≥0使得τ(e|x|(λ,∞))〈∞.将一些很有用的已知的Hilbert空间算子迹的不等式推广到τ-可测算子迹.特别是这些不等式蕴涵了n-元τ-可测算子的Clarkson不等式.同时还给出了τ-可测算子的广义平行四边形法则. 相似文献
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Daeshik Choi 《Linear and Multilinear Algebra》2018,66(2):280-284
In this paper, we present inequalities related to partial trace and block Hadamard product for positive semidefinite matrices. Some interesting results involving block matrices will be also derived. 相似文献
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Evans M. Harrell II Joachim Stubbe II 《Transactions of the American Mathematical Society》1997,349(5):1797-1809
In this article, we prove and exploit a trace identity for the spectra of Schrödinger operators and similar operators. This identity leads to universal bounds on the spectra, which apply to low-lying eigenvalues, eigenvalue asymptotics, and to partition functions (traces of heat operators). In many cases they are sharp in the sense that there are specific examples for which the inequalities are saturated. Special cases corresponding to known inequalities include those of Hile and Protter and of Yang.
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Viorel Catană 《Applicable analysis》2013,92(3):503-515
In this article we define two-wavelet localization operators corresponding to an irreducible and square-integrable representation of a locally compact Hausdorff group on a Hilbert space. The group structure admitting an irreducible and square-integrable representation which is related to β-Stockwell transform, that we shall use in this article β?∈?R have been introduced in Boggiatto et al. [P. Boggiatto, C. Fernandez, and A. Galbis, A group representation related to the Stockwell transform, Indiana Univ. Math. J. 58(5) (2009), pp. 2277–2296]. The Schatten–von Neumann norm inequalities of these two-wavelet localization operators are established. The traces and the trace class norm inequalities of the trace class two-wavelet localization operators are given. 相似文献