关于一个矩阵迹的不等式的注记

本文修正了［２］中的一个矩阵迹的不等式的一些错误，证明了ｔｒ［（Ａａ一Ｂａ）（Ａ一β一Ｂβ）］＜０当且仅当αβ＞０且Ａ≠Ｂ，ｔｒ［（Ａａ－Ｂａ）（Ａ－β－Ｂ－β）］＞０当且仅当αβ＜０且Ａ≠Ｂ，这里Ａ，Ｂ是ｎ×ｎ的Ｈｅｒｍｉｔｅ正定矩阵．     

关于“厄米特矩阵乘积的迹及其应用”一文的注记

本文改进[1]的主要结果,并指出了一些错误。     

关于矩阵迹的平均不等式

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...     

关于矩阵迹的不等式

讨论了满足条件R[A,B]≤1的矩阵和的平方的迹的不等式,并利用经典的H(o|¨)lder不等式和Minkowski不等式,证明了半正定Hermiter矩阵迹的H(o|¨)lder不等式和矩阵迹的Minkowski不等式的推广不等式.     

从矩阵迹关系过渡到算子迹关系的一个通用方法

本文给出了一个将矩阵迹的不等式推广为Ｈｉｌｂｅｒｔ空间中算子迹的不等式的方法，并用它较简捷地将矩阵论中Ｂｅｌｌｍａｎ问题的已有结果以及其它一些矩阵迹的不等式推广为算子迹的相应不等式。     

两个矩阵迹不等式及其证明

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。     

保持矩阵迹的乘法映射

设F是一个域 ,An,是一个乘法半群且满足 {aEij|i,j=1 ,2… ,n ,a∈F} An (F) ,其中Mn(F)定义F上所有n×n矩阵组成的乘法半群 ,本文证明了一个结果 :若f:AnF是一个保迹映射 ,则存在一个可逆阵P∈Mn(F)使得f(A) =PAP- 1 , A∈An由此推广了 [1 ]的一个结果 .     

矩阵指数的偏迹不等式

In this paper it is shown that if C is an n×n complex matrix and C^(k) is the k-th compound of C, 1≤k≤n, N = (n k) and if the eigenvalues of C^(k) are labeled inorder of decreasing magnitude |λ₁(C^(k))|≥λ₂(C^(k))|≥…≥λ_N(C^(k))|define the partial trace tr_i^(k)(C) by (?) Then for two n×n Hermrtian matrices A, B,with equality holds if A, B are commutative or k = n.     

一类矩阵迹不等式的证明

本文对一类新的矩阵迹不等式加以证明．并把该不等式看成是算术平均值和几何平均值下等式在矩阵迹运算上的推广．     

Z/(pr)上模p上三角矩阵的轨道

本文证明了由Birkhoff给出的有限Abel p-群的子群的标准矩阵表示所构造的从Z/pkZ×...×/pk的子群格到多重集{1k,2k,...,nk}(n3)的子集格之间的保秩保序映射ψ,在集中每一点的原象集均是Z/pk上的一般线性群的子群--模p上三角矩阵群的轨道.这个结果当k退化为1时,便可得到Knuth构造的关于子空间格到子集格的保秩保序映射也具有这种性质.     

直觉模糊矩阵幂序列的收敛准则

首先,给出直觉模糊矩阵幂的隶属度和非隶属度的表达形式.其次,定义直觉模糊矩阵的最小正周期数和收敛指数,得到单增的直觉模糊矩阵幂序列是收敛的结论.最后,给出直觉模糊矩阵幂序列收敛的两个充分条件.     

改进的PSB拟牛顿修正矩阵的收敛性

本文在已建立的一类新拟牛顿方程Ｂｋ＋１δｋ＝ｙｋ＝ｙｋ＋θｋ／δｋ＾Ｔｕ的基础上,证明了满足新拟牛顿方程的改进ＰＳＢ算法产生的拟牛顿修正矩阵序列在序列｛ｘｋ｝收敛于ｘ＾＊,｛δｋ｝一致性无关及二阶导数阵连续有界的条件下收敛于海色阵Ｇ（ｘ＾＊）。     

Application of the Trace Inequality to the Poisson Equation

The purpose of this paper is to show that solutions of the Poisson equation

An Explicit Formula and its Application to the Selberg Trace Formula

We prove that the explicit formula in a symmetric case for a triple (Z, [(Z)\tilde]\tilde{Z} , Φ) in Jorgenson-Lang’s fundamental class of functions holds for a larger class of (not necessarily differentiable or even continuous) test functions. As one of the most important applications, we show that the Selberg trace formula for a strictly hyperbolic cocompact Fuchsian group Γ is valid for a larger class of test functions. Further applications to growth estimates for the logarithmic derivative of the Selberg zeta function are considered.     

An Explicit Formula and its Application to the Selberg Trace Formula

We prove that the explicit formula in a symmetric case for a triple (Z, , Φ) in Jorgenson-Lang’s fundamental class of functions holds for a larger class of (not necessarily differentiable or even continuous) test functions. As one of the most important applications, we show that the Selberg trace formula for a strictly hyperbolic cocompact Fuchsian group Γ is valid for a larger class of test functions. Further applications to growth estimates for the logarithmic derivative of the Selberg zeta function are considered.     

The Cyclotomic Trace for S-Algebras

A functorial and categorical defined cyclotomic trace is given,extending the usual one for rings to ring spectra. There aretwo ingredients to this: first a cyclotomic trace is neededthat accepts a categorical input with few restrictive assumptions.This is important in its own right, since this allows one totransport rich structures through the cyclotomic trace. Secondly,a sufficiently nice model is needed for the category of finitelygenerated free modules which is functorial in the ring spectrum.     

The Norm and Regularized Trace of the Cauchy Transform

In this paper, the norm of the Cauchy transform C is obtained on the space L ²(D, dμ), where dμ = ω(|z|) dA(z). Also, (for the case ω ≡ 1), the first regularized trace of the operator C* C on L ²(Ω) is obtained. The results are illustrated by examples, with different specific choices of the function ω and the domain Ω.__________Translated from Matematicheskie Zametki, vol. 77, no. 6, 2005, pp. 844–853.Original Russian Text Copyright ©2005 by M. R. Dostanic.     

The relation between the Baum-Connes Conjecture and the Trace Conjecture

We prove a version of the L ²-index Theorem of Atiyah, which uses the universal center-valued trace instead of the standard trace. We construct for G-equivariant K-homology an equivariant Chern character, which is an isomorphism and lives over the ring ℤ⊂λ ^G ⊂ℚ obtained from the integers by inverting the orders of all finite subgroups of G. We use these two results to show that the Baum-Connes Conjecture implies the modified Trace Conjecture, which says that the image of the standard trace K ₀(C ^* _r (G))→ℝ takes values in λ ^G . The original Trace Conjecture predicted that its image lies in the additive subgroup of ℝ generated by the inverses of all the orders of the finite subgroups of G, and has been disproved by Roy [15]. Oblatum 10-IV-2001 & 18-X-2001?Published online: 15 April 2002     

The Trace in Banach Jordan Pairs

The algebraic trace form (as defined by O. Loos) of an element(x, y) of a (complex) Banach Jordan pair V, where x or y isin the socle, is equal to the sum of the products of all spectralvalues and their multiplicity. The trace form is calculatedfor two examples, the Banach Jordan pair of bounded linear operatorsbetween two Banach spaces, and the Banach Jordan pair of a quadraticform. Using analytic multifunctions, it is also shown that thecomplement of the socle of a Banach Jordan pair V is eitherdense or empty. In the last case, V has finite capacity. 1991Mathematics Subject Classification 17C65, 46H70.