U自共轭算子与自对偶次正常算子

本文通过对算子方程UA=A*U的讨论,给出了J.B.Conway于[1]中提出的自对偶次正常算子的一个内蕴性描述. 定义设H是可析的Hilbert空间,U是日上的酉算子,如果H上的算子A满足方程UA=A*U,则称A为U自共轭算子(U self adjoint,本文简记为U s.a.). U s.a.算子具有如下初等性质: 性质1 A是U s.a.算子,则σ(A)与σ_(?)(A)关于实数轴对称.当λ∈σ_(?)(A)时,A-λ与A-λ的Fredholm指标互为相反数,特别当λ为实数时,ind(A-λ)=0. 证显然,由方程UA=A*U,可知σ(A),σ.(A)是关于实数轴对称的.又根据U     

有界线性算子的Weyl定理的判定

令H为复的无限维可分的Hilbert空间, B(H)为H上有界线性算子的全体。称算子T∈B(H)满足Weyl定理, 若σ(T)\σw(T)=π₀₀(T), 其中σ(T)和σw(T)分别表示算子T的谱集与Weyl谱, π₀₀(T)={λ∈iso σ(T):0相似文献   

关于Vitali收敛定理的注记

在本文里,日表示一个复 Hilbert 空间,A(或带有下标的,如 A_1,A_k 等)总是表示 H 上的算子(即有界线性变换),I 为 H 上的恒等算子.假定 A 的谱为σ(A),D 是复平面上的固定区域(即连通开集),σ(A)D.对于 D 内的复解析函数 f,f(A)表示由通常的 Riesz-Dunford 积分([1],p.568)     

由算子定义的解析函数的卷积性质

通过H adam ard积定义了一个算子变换Iλ,μ,并利用其得到了单位开圆内解析函数类的新的子类S,λδμ(A,B),由此研究了函数类Sδλ,μ(A,B)的卷积性质,且考虑了单位开圆内的解析函数f(z)在算子Iλ,μ作用下的从属关系.     

一类本性正常算子的(U+K)轨道的闭包

讨论了一类本性正常算子的（U K）-轨道的闭包：（U K）（T）↑-。具体地讲，如果T是一个具有正常加紧形式的三角算子，且它的本性谱是完备的，对角线以上部分是紧的，得出结论：A∈L（H），A∈（U K）（T）↑-的充要条件是：（1）A∈Nor(H) K(H);(2)σ(A)增包含σ（T），σ0(A)增包含于σ0(T)，σe(A)=σe(T);(3)ind(λ-A）=ind(λ-T），A↓λ∈ρs-F(A)=ρs-F(A)=ρF(A);(4)nul（λ-A）≥nul(λ-T），A↓∈ρs-F(A);(5)如果λ∈σe(A)则rankE(λ；T）。除此之外，如果T是一个双三角的本性正常算子，它的谱σ（T）=σe(T)=σ是C的一个完备集，则A∈（U K)(T)↑当且仅当A满足：（1）A∈Nor(H) K(H);(2)σ（A）增包含σ（T）是完备的；（3）σe(A)=σe(A)=σe(T),且对任意的λ∈ρs-F(A),ind(λ-A）=0。     

自伴算子空间上满足[φ(A~2),A]+[A~2,φ(A)]=0的可加映射

运用算子论的方法,研究了自伴算子空间上满足[φ(A2),A]+[A2,φ(A)]=0的可加映射。如果可加映射φ:Bs(H)→Bs(H)满足对所有A∈Bs(H)有[φ(A2),A]+[A2,φ(A)]=0,那么存在λ∈R,可加映射f:Bs(H)→R,以及算子K∈Bs(H),使得对所有A∈Bs(H)有φ(A)=iAK-iKA+λA+f(A)I。即自伴算子空间上满足[φ(A2),A]+[A2,φ(A)]=0的可加映射是导子与可交换映射之和。     

关于Hilbert空间上算子解析函数的若干结果

设H是复Hilbert空间。对H上算子A与复解析函数/在某些通常假定下,f(A)表示由Riesz-Dunford积分定义的H上算子,遵循Ky Fan的近期工作,一些算子解析函数的补充结果被得到。这些结果之中包含有关于上半平面Ω解析函数f,f(Ω)Ω对应的算子解析函数f(A)的迭代定理,以及关于自单位开圆△到右半平面Π或自Π到△内解析函数f对应的算子解析函数f(A)的特征性质。     

微小摄动下SVEP与Weyl型定理的关系

设H为复的无限维可分Hilbert空间,B(H)为H上有界线性算子的全体.若σ(T)\σw(T)=πoo(T),则称T∈B(H)满足Weyl定理,其中σ(T)和σw(T)分别表示算子T的谱和Weyl谱,πroo(T)={λ∈isoσ(T):0dimN(T-λI)∞};当σ(T)\σw(T)∈roo(T)时,称T∈B(H)满足Browder定理.本文利用算子的广义Kato分解性质,刻画了算子在微小紧摄动下单值延拓性质(SVEP)与Weyl型定理之间的关系.     

算子及其函数的(R)性质的判定

令H为无限维复可分的Hilbert空间，H上有界线性算子的全体为B(H).用σ(T),σ_ab(T)和σ_a(T)分别表示为算子T∈B(H)的谱集，Browder本质逼近点谱和逼近点谱.称算子T∈B(H)满足(R)性质，若σ_a(T)σ_ab(T)=π₀₀(T),其中π₀₀(T)={λ∈iso σ(T)∶0相似文献   

拓扑一致降标与单值延拓性质

设H为Hilbert空间.算子T∈B(H)称作有单值延拓性质,若对任意一个开集U(∈)C,满足方程(T-λI)f(λ)=0((A)λ∈U)的惟一的解析函数为零函数.若存在整数d∈N使得当n≥d时,N(Tn)+R(T)=N(Td)+R(T)并且R(Tn)在R(Td)的算子值域拓扑中闭,称T当n≥d时有拓扑一致降标.本文给出了拓扑一致降标与单值延拓性质之间的关系,并利用算子的拓扑一致降标性质研究了单值延拓性质的稳定性.     

Markedness and its Interpretation in Language Use

Language markedness is a common phenomenon in languages, and is reflected from hearing, vision and sense, i.e. the variation in the three aspects such as phonology, morphology and semantics. This paper focuses on the interpretation of markedness in language use following the three perspectives, i.e. pragmatic interpretation, psychological interpretation and cognitive interpretation, with an aim to define the function of markedness.     

低渗透非均质砂岩油藏启动压力梯度研究

理论推导与室内实验相结合,建立了低渗透非均质砂岩油藏启动压力梯度确定方法。首先借助油藏流场与电场相似的原理,推导了非均质砂岩油藏启动压力梯度计算公式。其次基于稳定流实验方法,建立了非均质砂岩油藏启动压力梯度测试方法。结果表明:低渗透非均质砂岩油藏的启动压力梯度确定遵循两个等效原则。平面非均质油藏的启动压力梯度等于各级渗透率段的启动压力梯度关于长度的加权平均;纵向非均质油藏的启动压力梯度等于各渗透率层的启动压力梯度关于渗透率与渗流面积乘积的加权平均。研究成果可用于有效指导低渗透非均质砂岩油藏的合理井距确定,促进该类油藏的高效开发。     

On Tragic Consciousness In The Works By Ernest Hemingway

As an American modern novelist who were famous in the literary world, Hemingway was not a person who always followed the trend but a sharp observer. At the same time, he was a tragedy maestro, he paid great attention on existence, fate and end-result. The dramatis personae's tragedy of his works was an extreme limit by all means tragedy on the meaning of fearless challenge that failed. The beauty of tragedy was not produced on the destruction of life, but now this kind of value was in the impact activity. They performed for the reader about the tragedy on challenging for the limit and the death.     

Achieving Unusual States of Matter Under High Pressure

正The periodicity of the elements and the non-reactivity of the inner-shell electrons are two related principles of chemistry,rooted in the atomic shell structure.Within compounds,Group I elements,for example,invariably assume the+1 oxidation state,and their chemical properties differ completely from those of the p-block elements.These general rules govern our understanding of chemical structures and reactions.Using first principles calcula-     

Exchange-Correlation and Electronic Excitation Energies from Pairing Matrix Fluctuations

We have developed an adiabatic connection to formulate the ground-state exchange-correlation energy in terms of pairing matrix linear fluctuations.This formulation of the exchange-correlation energy opens a new channel for density functional approximations based on the many-body perturbation theory.We illustrate the potential of such approaches with an approximation based on the particle-particle Random Phase Approximation(pp-RPA).This re-     

Density Functional Theory for the Response of Periodic Systems to Electric Fields Based on the Vector Potential Approach

正The electronic and nuclear(structural/vibrational)response of 1D-3D nanoscale systems to electric fields gives rise to a host of optical,mechanical,spectral,etc.properties that are of high theoretical and applied interest.Due to the computational difficulty of treating such large systems it is convenient to model them as infinite and periodic(at least,in first approximation).The fundamental theoretical/computational problem in doing so is that     

On the Thermodynamic Limit for Responses to Static Electromagnetic Fields

For molecular systems,the quantum-mechanical treatment of their responses to static electromagnetic fields usually employs a scalar-potential treatment of the electric field and a vector-potential treatment of the magnetic field.Although the potential for each field separately is associated with the choice of an(unphysical)origin,the precise choice of the origin for the electrostatic field has little consequences for the results.This is different for the     

An affordable accurate evaluation of the binding conformations predicted by molecular docking studies in bio-system

Franck-Condon factors bridge the gap between theoretical modeling and experimental observations for molecular electronic spectroscopy and electron transfer.Under the displaced harmonic oscillator approximation,multidimensional Franck-Condon factors are decomposed into a product of many one-dimensional(1D)Franck-Condon(FC)factors,and each 1D-FC factor is associated with one Huang-Rhys factor that determines the leading contribution of     

Call for Papers

<正>"The Journal of Shanghai Normal University:Mathematics"is published by Shanghai Normal University as regular issues of The Journal of Shanghai Normal University each year from 2014 in English.The editors-in-chief of the issues are professors Yuhao Cong and Maoan Han.The Journal of Shanghai Normal University was started in 1958 with     

Journal of Donghua University ( English Edition) Contents of Volume 31

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