序列次可分解算子的不变子空间

利用S. Brown技巧,在稍微增加了一点谱的厚度的情形下证明了Mohebi-Radjabalipour猜想,得到了序列次可分解算子的两个不变子空间定理. 作为特殊情形该结果包含了H. Mohebi 和 M. Radjabalipour得到的一个重要的不变子空间定理.     

复平面上解析Banach空间的拟不变子空间

讨论复平面上解析Banach空间具有任意指标的拟不变子空间的存在性问题.首先给出一类复平面上解析Banach空间存在任意指标拟不变子空间的判定定理.作为应用,证明了Fock型空间F~p(C)={f∈Hol(C):1/π∫_C|f(z)|~pe~(-|z|~2)dA(z)+∞,1≤p+∞}与Hilbert空间H={f∈Hol(C):1/π∫_C|f(z)|~2e~(-|z|)dA(z)+∞}具有任意指标的拟不变子空间.     

一类本质正规算子的稳定不变子空间

在本文中 ,我们给出了一类本质正规算子的稳定不变子空间的特征 .即 ,T∈ L( H2 ( Ω;μ) )且满足1 ) T是本质正规算子 ;2 )σ( T) =Ω,σe( T) = Ω,σp( T) =Ω ;3) ind( T-z) =n,z∈Ω;4 ) minind( T-z) =0 ,z∈ Ω.M是 T的非平凡的不变子空间 ,则 M是 T的稳定不变子空间当且仅当 dim M<∞ and dim M⊥ =∞     

算子的一种更弱的相似性与互逆性

§1.定义与符号设H是可分的复Hilbert空间,B(H)表示H上全体有界算子的代数。对于A∈B(H),我们分别以R(A)、N(A)、{A}′及LatA表示它的值域、零空间、换位及不变子空间格。对于T,S∈B(H),如果有内射的稠值域的算子X,Y∈B(H),使得TX=XS,YT=SY,则说T与S是拟相似的。算子的拟相似性已经有丰富的内容。与拟相似概念有类似性的是算子互为拟仿射逆的概念[1],即:若T,S∈B(H),如果有内射的稠值域的算子X,Y∈B(H),使得TXS=X,SYT=Y,则说T与S互为拟仿射     

Bloch空间上的Cesaro算子是有界的

记B={f:f∈H(D),‖f‖B＜∞}为Bloch空间，其中‖f‖B=sup |x|＜1(1-|z|^2)|f′(z)|,对于f(z)=^∞∑(k-0)akz^k∈B，定义Cesaro算子B为(Bf)(z)=^∞∑(n=0)(1/(n 1) ^n∑(k=0)ak)z^n在这篇文章中，我们将证明如下结果。     

算子的拟仿射变换与拟仿射逆

设H是可分的复Hilbert空间,B(H)是H上全体有界线性算子的代数。以后把B(H)的元简单地叫做算子。对于算子T∈B(H),用R(T)、N(T)、σ(T)及LatT分别表示其值域、零空间、谱及不变子空间的格。算子X∈B(H)叫做拟仿射,如果它满足N(X)=N(X~*)={0}。若T、S、X∈B(H),X是拟仿射,TX=XS,则S叫做T的拟仿射变换。与此类似的一个概念是:若TXS=X,X是拟仿射,则T(S)叫做S(T)的左(右)拟仿射逆([1])。在§1中,找到了有左(右)拟仿射逆的算子是可逆的一些     

标准算子代数上满足某些等式的广义导子的刻画(英文)

令H为复数域C上的Hilbert空间,A为H上的标准算子代数.设δ:A→B(H)是线性映射.本文证明了,如果对任意A∈A成立δ(AA~*A)=δ(A)A~*A-Aδ(A~*)A+AA~*δ(A),则存在λ∈C及算子S,T∈B(H)满足S+T=λI,使得对所有的A∈A都有δ(A)=SA-AT.     

关于序列次可分解算子的不变子空间

得到了关于序列次可分解算子的一个不变子空间定理，推广了H.Mohebi和M.Rajiabalipour在1994年得到的一个不变子空间定理，并且举例说明存在l2上的有界线性算子T。它有无穷多个变子空间，但是它的不变子空间格Lat(T)不丰富。     

代数Paranormal算子的谱

若任给x∈H,‖Tx‖~2≤‖T~2x‖·‖x‖,T∈B(H)称为是一个paranormal算子.T∈B(H)称为代数paranormal算子,若存在非常值复值多项式p,使得p(T)为para- normal算子.本文利用代数paranormal算子的谱集的特点,研究了代数paranormal算子以及该算子的拟仿射变换的Weyl型定理.     

算子矩阵代数的自反性和超自反性

本文总假定 H 是可分的 Hilbert 空间;L(H)表示 H 上有界线性算子全体;而 L(?)(H)表示 L(H)上σ-ω算子拓扑连续的线性泛函全体.设(?)L(H)为σ-ω算子拓扑闭的子代数,(?)称为自反的是指(?)=Alg Lat(?)={T∈L(H):TE(?)E (?)E∈Lat(?)},其中 Lat(?)是(?)的不变子空间格.(?)称为超自反的是指存在常数 K>0,使对任意的 T∈L(H)有 d(T,(?))≤K sup{‖P_M~(?)TP_M‖∶M∈Lat(?)}.其中 P_M 是指到 M 上的自伴投影。有关算子代数的超自反性已有一些结果,例如见     

Power bounded operators and supercyclic vectors

By the well-known result of Brown, Chevreau and Pearcy, every Hilbert space contraction with spectrum containing the unit circle has a nontrivial closed invariant subspace. Equivalently, there is a nonzero vector which is not cyclic.

We show that each power bounded operator on a Hilbert space with spectral radius equal to one has a nonzero vector which is not supercyclic. Equivalently, the operator has a nontrivial closed invariant homogeneous subset. Moreover, the operator has a nontrivial closed invariant positive cone.

     

Invariant subspaces for polynomially bounded operators

Let T be a polynomially bounded operator on a Banach space X whose spectrum contains the unit circle. Then T∗ has a nontrivial invariant subspace. In particular, if X is reflexive, then T itself has a nontrivial invariant subspace. This generalizes the well-known result of Brown, Chevreau, and Pearcy for Hilbert space contractions.     

On invariant subspaces for polynomially bounded operators

We discuss the invariant subspace problem of polynomially bounded operators on a Banach space and obtain an invariant subspace theorem for polynomially bounded operators. At the same time, we state two open problems, which are relative propositions of this invariant subspace theorem. By means of the two relative propositions (if they are true), together with the result of this paper and the result of C.Ambrozie and V.Müller (2004) one can obtain an important conclusion that every polynomially bounded operator on a Banach space whose spectrum contains the unit circle has a nontrivial invariant closed subspace. This conclusion can generalize remarkably the famous result that every contraction on a Hilbert space whose spectrum contains the unit circle has a nontrivial invariant closed subspace (1988 and 1997).     

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.     

积分半群的Lumer—Phillips定理

一个n次积分半群S(t)如果满足‖S^(n)(t)x‖≤‖x‖,A↓t≥0,x∈D(A^n),我们就称S(t)是一压缩的n次积分半群,其中A为半群S（t)的生成元。在本中,我们完全刻划了n次压缩积分半群的特征,给出了n次压缩积分半群的Lumer-Phillips定理。     

算子n次方根的惟一性

B(H)表示定义在希尔伯特空间H上的所有有界线性算子的全体。对于A∈B(H),其中σ(A)和W(A)分别表示算子A的谱和数值域,N表示自然数集。关于算子A的n(n∈N)次方根,本文的主要结果是:(1)若σ(A)∩(-∞,0]=φ,则A有惟一的n次方根B∈B(H)且σ(B)(?)~(2/n)~o;(2)若(?)∩(-∞,0]=φ,则A有惟一的n次方根B∈B(H)且(?)(2/n)~o这里,S_(1/n)={λ∈C‖argλ|≤(1/2n)π}且S_(1/n)~o表示集合S+(1/n)的内部。     

Rank theorems of operators between Banach spaces

Let E and F be Banach spaces, and B(E,F) all of bounded linear operators on E into F. Let T0∈B(E,F) with an outer inverse T#0∈B(F,E). Then a characteristic condition of S=(I+T#0(T-T0))-1T#0 with T∈B(E,F) and ‖T#0(T-T0)‖<1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.     

解析函数与Lipschitz条件

研究了解析函数与Lipschitz条件,得到了如下两个结果:(i)设D是一平面区域,f(z)在D中解析,00,对任意z∈D有|f′(z)|≤md(z,D)k-1,则f∈Lipk(D)且‖f‖k≤cmk,其中c=c(D)是仅与D有关的常数.     

THE EXISTENCE OF RADIAL LIMITS OF ANALYTIC FUNCTIONS IN BANACH SPACES

Let X be a comPlex Banach space and let D be the open unit disc in the complex plane.We shall denote by H"(D, X) the Banach space consisting of all uniformly bounded X-vaued analytic functions defined on D equipped with the norm llflloo = suP lIf(z)Il. Az eDcomplex Banach space X is said to have the analytic Radon-NikOdym property if eachelemellt f E Hoo(D,X) has radial limits almost everywhere on the torus T = {e": 0 E[0, 2x]} (see [1]), this means that for almost all 0 C [0,27l, 9W…