拟绝对-*-κ-仿正规算子的谱性质

引入了拟绝对-*-k-仿正规算子,获得了拟绝对-*-k-仿正规算子的一个充要条件.并证明了拟绝对-*-k-仿正规算子在0≤k≤1上是有限上升的,作为此性质的应用,证明了若T是拟绝对-*-k-仿正规算子,其中0≤k≤1,则Weyl谱和本质近似点谱的谱映射定理成立.最后证明了若T是拟绝对-*-k-仿正规算子,其中0≤k≤1,则σ_(ja)(T)\{0}=σ_a(T)\{0}.     

复合形在欧氏空间中的实现问题Ⅲ

<正> 设 K 是一个有限单形复合形,我们恒可视 K 为一充分高维数 N 的欧氏空间中的欧氏复合形,此时其所定空间将记为(?).在研究 K 是否可实现于某一确定维数 m 的欧氏盘间R~m 中的时候,我们曾引进下面的一些定义(见[1],记号略有不同):     

重单值扩张算子的谱结构与拟相似

本文证明了,若T是重单值扩张算子,则若T1是重单值扩张（C）算子,T2是任一有界线性算子,T1与T2拟相似,则σe（T1）＝σk（T1）σk（T2）＝σe（T2）     

本质正规算子的模小紧相似

本文证明了一类本质正规算子Ａ＇（Ω＇;１）（Ｔ∈Ａ＇（Ω＇;１）,如果Ｔ满足（１）Ｔ,Ｔ｜Ｈ（Ｔ）分别是本质正规算子;（２）σ（Ｔ）＝Ω,ρＦ（Ｔ）∩σ（Ｔ）＝Ω;（３）ｉｎｄ（Ｔ－λ）＝－１,ｎｕｌ（Ｔ－λ）＝０,λ∈Ω＇;（４）σ（Ｔ｜Ｈ（Ｔ））是一完全集,这里Ω＇是一连通的解析Ｃａｕｃｈｙ域, Ｈｌ（Ｔ）＝ Ｖ｛ｋｅｒ（Ｔ－λ）＊：λ∈ρｒｓ－Ｆ（Ｔ）｝是模小紧相似的．     

THE （u＋К）-ORBIT OF ESSENTIALLY NORMAL OPERATORS AND COMPACT PERTURBATIONS OF STRONGLY IRREDUCIBLE OPERATORS

Let Н be a complex,separable,infinite dimensional Hilbert space,T∈L(Н),(U+κ)(T) denotes the (U+κ)-orbit of T,i.e.,(U+κ)(T)={R^-1 TR:R is invertible and of the form unitary plus compact}.Let Ω be an analytic and simply connected Cauchy domain in C and n∈N,A（Ω,n）denotes the class of operators,each of which satisfies (i) T is essentially normal;(ii)σ(T)=Ω^-,ρF（T）∩σ（T）=Ω;（iii）ind(λ-T)=-n,nul(λ-T)=0,(λ∈Ω）。it is proved that given T1,T2∈A(Ω,n）and c&gt;0,there exists a compact operator K with ||K||&lt;ε such that T1+K∈(u+κ)(T2),this result generalizes a result of P.S.Guinand and L.Marcoux[6,15],Furthermore,the authors give a character of the norm closure of (u+κ)(T),and prove that for each T∈А(Ω,n）,there exists a compact (SI) perturbation of T whose norm can be arbitrarily small.     

向量值树鞅及若干不等式

证明了向量值树鞅的若干不等式.主要结果是如下不等式若X同构于q一致凸空间(2≤q＜∞),则对每个X值的树鞅f=(ft,t∈T)α≥1和max(α,q)≤β＜∞成立‖(S(q)t(f),t∈T)‖ Mα∞≤Cαβ‖f‖ Pαβ‖(σ(p)t(f),t∈T)‖ Mα∞≤Cαβ‖f‖pαβ其中Cαβ是只依赖于α和β的常数.     

Total Valuation Rings of Ore Extensions

We consider extensions of a total valuation ring V of a skew field K to the Ore extension K(X;σ, δ) for an endomorphism σ of K and a σ-derivation δ. It is shown that there exists an extension R of V with X ∈ R, such that ${\overline X}$ is transcendental over V/J(V) if and only if (σ,δ) is compatible with V, where ${\overline X} = X + J(R^(1))$ . In the case V is invariant, it is established that there is an invariant extension R of V in K(X;σ,δ) such that ${\overline X}$ is transcendental if and only if σ(a)V = aV and δ(a) ∈ aV for all a ∈ K.     

A Semigroup of Theories and Its Lattice of Idempotent Elements

Algebra and Logic - On the set of all first-order theories T(σ) of similarity type σ, a binary operation {·} is defined by the rule T · S = Th({A × B | A |= T and B |= S})...     

形式矩阵环上的σ-双导子和σ-交换映射

令(R N M S)是一个具有零迹理想的形式矩阵环,σ是K的一个满足σ(E₁₁)=E₁₁,σ(E₂₂)=E₂₂的自同构.本文确定了K的σ-双导子和σ-交换映射的一般形式,证明了在一定条件下K的每个σ-双导子都可以表示成一个外σ-双导子与一个内σ-双导子的和.此外,本文给出了K的任意σ-双导子(σ-交换映射)是内σ-双导子(真σ-交换映射)的一个充分条件.     

Possible Spectrums of 3×3 Upper Triangular Operator Matrices

Let H1, H2 and H3 be infinite dimensional separable complex Hilbert spaces. We denote by M(D,E,F) a 3×3 upper triangular operator matrix acting on H1⊕H2⊕H3 of the form M(D,E,F)=(A D E 0 B F 0 0 C). For given A ∈ B(H1), B ∈ B(H2) and C ∈ B(H3), the sets UD,E,F σp(M(D,E,F)), ∪D,E,F σr(M(D,E,F)), ∪D,E,F σc(M(D,E,F)) and ∪D,E,F σ(M(D,E,F)) are characterized, where D ∈ B(H2,H1), E ∈ B(H3, H1), F ∈ B(H3, H2) and σ(·), σp(·), σr(·),σc(·) denote the spectrum, the point spectrum, the residual spectrum and the continuous spectrum, respectively.     

Quotient rings of finitely generated P.I. Algebras

This paper generalizes properties which hold for localization of Azumaya algebras, in two directions. Firstly, fully left bounded left Noetherian rings, especially finitely generated Noetherian algebras, are considered. It is noted that for such rings every idempotent kernel functor a is symmetric, i.e. the filter T(σ) of a-dense left ideals has a basis of a-dense ideals. A prime ideal P of a f.l.b.l.N. ring R is localizable if and only if it is the intersection of the P-critical left ideals. In case R is a finitely generated algebra over its (Noetherian) center C, we apply the technique of “descent” of kernel functors. If a is a symmetric kernel functor such that R(A n c) S T(σ) for every A G T(σ) and such that a has property (T) then there is a kernel functor a’ on C-modules such that Qσ (R) ?Q? ,(R). If P is a prime ideal of R then σ_- descends to C if and only if P is localizable. Secondly, a class of rings is described in terms of the Zariski topology on Spec. The imposed condition is weaker than maximal centrallity and does not imply fully left boundedness either, but the good properties of Spec R in case R is an Azumaya algebra are preserved.     

环上的σ-导子

本文研究了σ－导子的扩张问题，并且在本原环上刻化了s－导子。     

Dynamical systems disjoint from any minimal system

Furstenberg showed that if two topological systems and are disjoint, then one of them, say , is minimal. When is nontrivial, we prove that must have dense recurrent points, and there are countably many maximal transitive subsystems of such that their union is dense and each of them is disjoint from . Showing that a weakly mixing system with dense periodic points is in , the collection of all systems disjoint from any minimal system, Furstenberg asked the question to characterize the systems in . We show that a weakly mixing system with dense regular minimal points is in , and each system in has dense minimal points and it is weakly mixing if it is transitive. Transitive systems in and having no periodic points are constructed. Moreover, we show that there is a distal system in .

Recently, Weiss showed that a system is weakly disjoint from all weakly mixing systems iff it is topologically ergodic. We construct an example which is weakly disjoint from all topologically ergodic systems and is not weakly mixing.

     

拟连续Domain的若干拓扑性质

对拟连续Domain D证明了:(1)双拓扑空间(D,σ(D),(D))为两两完全正则空间;(2)若D有可数基,则(max(D),σ(D)max(D))为正则空间当且仅当它为Polish空间;(3)拓扑空间(D,σb(D))为零维Tychonoff空间,其中σb(D)为D上Scott拓扑的b-拓扑。     

A multidimensional central limit theorem with speed of convergence for axiom a diffeomorphisms

Let T:X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f:X → R^d is a Hlder continuous function with ∫_X^fdm = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ²:=σ² （f ） such that S^fn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ² . Moreover, there exists a real number A > 0 such that, for any integer n ≥ 1,Π( m*（ 1√ nS f n ）,N （0,σ² ） ≤A√n, where m*（1√ n S^fn）denotes the distribution of 1√ n S^fn with respect to m, and Π is the Prokhorov metric.     

Mn(C)中的不可约性

对于Mn(C)(所有n×n矩阵的全体)中的不可约矩阵得到以下结果:对于任意A∈Mn(C),设λ1,λ2,…,λm为A的所有特征值,这里m≤n而且当i≠j时,λi≠λj.则A是不可约的当且仅当任意P∈A'(A),P*=P=P2,有σ(P|ker(A-λ1))=σ(P|ker(A-λ2))=…=σ(P|ker(A-λm))为单点集.     

Alternative proof of the a priori tan Θ theorem

Let A be a self-adjoint operator in a separable Hilbert space. We assume that the spectrum of A consists of two isolated components σ₀ and σ₁ and the set σ₁ is in a finite gap of the set σ₁. It is known that if V is a bounded additive self-adjoint perturbation of A that is off-diagonal with respect to the partition spec(A) = σ₀ ∪ σ₁, then for \(\left\| V \right\| < \sqrt 2 d\), where d = dist(σ₀, σ₁), the spectrum of the perturbed operator L = A+V consists of two isolated parts ω₀ and ω₁, which appear as perturbations of the respective spectral sets s0 and s1. Furthermore, we have the sharp upper bound ||EA(σ₀) - EL(ω₀)|| ≤ sin (arctan(||V||/d)) on the difference of the spectral projections E_A(σ₀)) and E_L(ω₀)) corresponding to the spectral sets σ₀ and ω₀ of the operators A and L. We give a new proof of this bound in the case where ||V|| < d.     

Banach空间积分双半群的生成条件

研究Banach空间中积分双半群的生成条件.利用算子A的豫解算子,给出了积分双半群T(t)的生成定理.结果表明:如果对任意的x∈X,f∈X*,以及A|λ]<δ,λ∈ρ(A),有∈Lp(R),则存在算子族S(t),t∈R,S(t)强连续且满足积分双半群的定义.     

套代数上的σ-双导子和σ-可交换映射

本文证明了当dim 0_+≠1或dim H_-~⊥≠1时,套代数γ(N)上的每一个σ-双导子都是σ-内双导子.作为应用,给出了满足条件f(X)X=σ(X)f(X)的线性映射f的形式.     

分块奇异线性模型及其导出的奇异线性模型间的最小范数二次无偏估计等价性研究

本文考虑一般线性模型A=(y,X1β1 X2β2,σ^2V)及其导出线性模型，其中V是已知的非负定矩阵，X=(X1：X2)是已知的设计矩阵，给出了线性模型A及其导出线性模型间最小范数二次无偏估计间差的表达式，更进一步，建立了线性模型A及其导出线性模型间最小范数二次无偏估计相等的充分必要条件。