B(X)上保持约当积的固定点的满射

设B(X)是维数大于等于3的复Banach空间X上有界线性算子全体构成的代数.设A∈B(X),若Ax=x,则称x∈X是算子A的固定点.Fix(A)表示A的所有固定点的集合.本文刻画了B(X)上保持算子的Jordan积的固定点的满射.     

加权移位与BIR算子

长期来,人们在追求Jordan标准型在无穷维空间上的推广,虽然困难很大,进展不多,但仍然出现了许多好工作。在不少工作中,似乎认为单胞算子是Jordan块的最合适的推广。实际上,在无穷维空间中,单胞算子起不了有限维空间中Jordan块的作用,而作为Jordan块的推广,也许应该是报告[1]中所说的BIR算子。但Jordan块与单胞算子所具有的性质,是否BIR算子也都具有呢?本文的一个主要目的,是在加权移位范围内,对BIR算     

一类具幂指积系数微分算子谱的离散性

应用算子直和分解法和二次型比较的方法,研究了一类具幂指积系数微分算子谱的离散性,得到了该类微分算子的谱是离散的一些充分条件.     

具有可积系数的高阶J自伴微分算子的离散谱的条件

研究了一类具有可积系数的高阶J-自伴微分算子谱离散性的充分条件与必要条件,为判断这一类微分算子谱的离散性提供了若干准则.     

一类具欧指积系数微分算子谱的离散性(英文)

利用算子直和分解的方法和二次型估计的方法,研究了一类具欧指积系数微分算子谱的离散性,得到了其谱是离散的一些充分条件.     

一类串联可修复系统的稳态解

本文讨论了一类具有两不同部件串联的可修复系统。利用系统算子生成的Banach空间中的正压缩C_o半群的性质,证明了系统的非负稳态解恰是系统算子的0本征值所对应的规范化后的本征向量；同时通过对系统算子谱点分布情况的分析,证明了系统算子的谱点均位于复平面左半平面且在虚轴上除0点外无其它谱,作为线性算子半群稳定性的—个直接结果,得出了该串联可修复系统的渐近稳定性。     

有两种修复方法的复杂可修复系统解的渐近稳定性

讨论了两种修复方法的系统解的渐近稳定性.证明了系统在Banach空间中生成正压缩c0半群,系统的非负稳定解恰是系统算子0本征值对应的本征向量,系统算子的谱点均位于复平面的左半平面且在虚轴上除0外无谱.     

具有临界和非临界操作错误的人机系统的渐近稳定性

讨论具有临界和非临界操作错误的可修复人机系统．利用系统算子生成的Banach 空间中的正压缩C0半群的性质,证明了此系统的唯一非负时间依赖解恰是系统算子0本征值对应的规范化后的本征向量;同时通过对系统算子谱点分布情况的分析,证明了系统算子的谱点均位于复平面左半平面且在虚轴上除0点外无其它谱,作为线性算子半群稳定性的一个直接结果,得出了该可修人机系统的渐近稳定性．     

一类抽象动力系统的C0群性质及其在迁移理论中的应用

本文研究一类抽象动力系统的性质.使用Hilbert空间的分解方法,获得了主算子的谱和相应的群的表示;使用有界线性算子的扰动理论,获得了抽象动力算子的谱分解.作为应用,研究了迁移理论中的一类积-微分方程.     

一类Schr(o)dinger算子的谱范围

针对半直线上可积势对应的Schr(o)dinger算子,研究A-函数和谱之间的关系,利用复分析中保形变换的方法给出了谱测度关于A-函数的局部表示,进而得到算子的谱范围,该结论说明了这一类Schr(o)dinger算子是下半有界的.     

Characterizations of the support function of the numerical range of the product of positive contractions

In this note, the numerical range and spectrum of the product of positive contractions are discussed. We shall establish some characterizations of the support function of the numerical range of the product of positive contractions.     

Pseudo Jordan domains and reflecting Brownian motions

Summary The manifold metric between two points in a planar domain is the minimum of the lengths of piecewiseC ¹ curves in the domain connecting these two points. We define a bounded simply connected planar region to be a pseudo Jordan domain if its boundary under the manifold metric is topologically homeomorphic to the unit circle. It is shown that reflecting Brownian motionX on a pseudo Jordan domain can be constructed starting at all points except those in a boundary subset of capacity zero.X has the expected Skorokhod decomposition under a condition which is satisfied when G has finite 1-dimensional lower Minkowski content.     

Pre-compactness of isospectral sets for the neumann operator on planar domains

The Neumann operator maps the boundary value of a harmonic function tc its normal derivative. The inverse spectral properties of the Neumann operator associated to smooth, planar, Jordan curves are studied. The Riemann mapping theorem is used tc parametrize the set of planar Jordan curves by positive functions on the unit circle. By studying the zeta function associated to the spectrum, it is shown that isospectral sets of these functions are pre-compact in the topology of the L²-Sobolev space of order 5/2 - [euro]. Spectral criteria are given for the limiting curves of an isospectral set to be Jordan. A spectrally determined lower bound on the area of the interior of the curve is given.     

Contractions of Low-Dimensional Nilpotent Jordan Algebras

In this article, we classify the laws of three-dimensional and four-dimensional nilpotent Jordan algebras over the field of complex numbers. We describe the irreducible components of their algebraic varieties and extend contractions and deformations among their isomorphism classes. In particular, we prove that 𝒥² and 𝒥³ are irreducible and that 𝒥⁴ is the union of the Zariski closures of the orbits of two rigid Jordan algebras.     

The Quadratic Numerical Range of an Analytic Operator Function

We introduce a new concept of numerical range for analytic operator functions. This so-called quadratic numerical range is induced by a decomposition of the underlying Hilbert space. Like the classical numerical range of an operator function, it is not convex, it has the spectral inclusion property, and it provides resolvent estimates and estimates for the lengths of Jordan chains in boundary points having the exterior cone property. As the quadratic numerical range is contained in the numerical range, it yields tighter enclosures for the eigenvalues and the spectrum of analytic operator functions.     

The Jordan plane over a field of positive characteristic

The primary spectrum and the automorphism group of the Jordan plane over a field of nonzero characteristic are described. The problem of extending a prime ideal of the center of the Jordan plane to a primary ideal of the entire algebra is considered.     

Die struktur endlicher schwach abgeschlossener Jordanalgebren Teil II. Diskrete Jordanalgebren

In the preceding note [6] we reduced the study of continuous finite weakly closed Jordan algebras to real associative W^*-algebras of type II₁. Here we treat the remaining case of discrete finite weakly closed Jordan algebras and describe them completely by finite dimensional simple formally real Jordan algebras and by simple formally real Jordan algebras of quadratic forms of real Hilbert spaces. Jacobsons theory of Jordan algebras with minimum condition combined with W^*-algebra techniques constitutes an essential tool in the proof.     

Jordan higher derivable maps on triangular algebras by commutative zero products

In this paper, the structure of Jordan higher derivable maps on triangular algebras by commutative zero products is given. As an application, the form of Jordan higher derivable maps of nest algebras by commutative zero products is obtained.     

三角代数上的Jordan零点ξ-Lie可导映射

给出了三角代数上Jordan零点ξ-Lie可导映射的结构.作为应用,得到了套代数上Jordan零点ξ-Lie可导映射的具体形式.