共查询到19条相似文献,搜索用时 140 毫秒
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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. 相似文献
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设H是一个可分的Hilbert空间,(?)(H)是H上的有界线性算子全体.对 A∈(?)(H),(?)’(A)={B∈(?)(H):AB=BA},rad(?)’(A)表示(?)’(A)的Jacob son根.本文首先举例说明了存在Cowen-Douglas算子T,商代数(?)’(T)/rad(?)’(T) 可以是不交换的.在给出了使得(?)’(T)/rad(?)’(T)交换的充分条件之后,证明了使得 (?)’(T)/rad(?)’(T)交换的Cowen-Douglas算子在Bn(Ω)中是稠密的.对Bmn(Ω),得到了类似的结果。 相似文献
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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 相似文献
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薛以锋 《数学年刊A辑(中文版)》1989,(4)
设H是复的无限维可分Hilbert空间,记L(H)为H上所有有界线性算子所生成的代数。本文讨论了L(H)中的B_n(Ω)-类算子和单位算子I_H所生成的C~*-代数的一些性质,并由此构造出了B_n(Ω)-类算子分解为不可约的B_(n_i)(Ω)-类算子直和的具体形式,其中,n=sum from i=1 to m n_i,m是T与I_H所生成的C~*-代数的级。 相似文献
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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. 相似文献
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本文研究Pontrjagin空间上一般算子代数弱闭和一致闭的等价条件,得到定理:设C0(U),C1(U,L,R,D,V),C2a(U),C2b(U,R),C3a(U),C3b(U,R)分别是Ⅱk空间上第0,Ⅰ,Ⅱa,Ⅱb,Ⅲa和Ⅲb类的算子代数,则(1)C0(U),C2a(U)或C3a(U)为一致闭(弱闭)的等价条件是U是Hibert空间G上的C*-代数(W*-代数;(2)C1(U,L,R,D,V)为一致闭(弱闭)的等价条件是U是Hibert空间H上的C*-代数(W*-代数),并且R是闭子空间,V是闭算子,L对称闭的;(3)C2b(U,R)或C3b(U,R)为一致闭(弱闭)的等价条件是U是Hibert空间H上的C*-代数(W*-代数),并且R是闭子空间. 相似文献
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设算子代数A B(H),μ(A)表示A中的部分等距算子全体,若p是A到B(H)的线性映射,且对任意的UEu(A),有叫U)(kecU)Gr“hCr,则称 是A上的μ-核值保持映射。本文将证明:Nest代数的Jacobson根上的范数拓扑连续的μ-核值保持映射是广义内导子。 相似文献
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Daoxing Xia 《Integral Equations and Operator Theory》1985,8(6):854-881
In this present paper, the almost Lie algebra of operators is introduced. By a natural homomorphism, this almost Lie algebra of operators is mapped to a Lie algebra. By choosing a basis in this Lie algebra, a bilinear functional on the enveloping algebra of this Lie algebra is defined through the trace of some operators which are related to the communtators. A general trace formula is obtained by means of the partial derivatives and symmetric operation in the enveloping algebra. More concrete formula is also obtained in terms of a linear functional on the commutators in some special cases. 相似文献
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In this paper we study the Banach algebra of singular integral operators with piecewise continuous coefficients and a Carleman orientation-reversing slowly oscillating shift on the Lebesgue space with a power weight on the unit circle. The slow oscillation of the shift derivative, in contrast to the classic assumption on its piecewise continuity, leads to the appearance of massive local spectra for the considered operators. Applying localization techniques and the theory of Mellin pseudodifferential and associated limit operators, we construct a symbol calculus for the above-mentioned operator algebra and find a Fredholm criterion and an index formula for the operators in this algebra in terms of their symbols.Partially supported by CONaCYT grant, Cátedra Patrimonial, No. 990017-EX and by CONACYT project 32726-E, México.Partially supported by F. C. T. grant Praxis XXI/2/2.1/MAT/441/94, Portugal. 相似文献
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本文定义了(f,T)-相容对(B,H),利用这样的相容对可以给出一个辫子张量 范畴和一个量子Yang-Baxter方程的解,并且通过扭曲Hopf代数B的乘法,构造 Yetter-Drinfeld范畴中HHyD的Hopf代数. 相似文献
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In this paper we consider several fundamental operators in complex Clifford algebra and show the close relationship of these operators. We also discuss a representation of the Lie algebra s[(z; C) and get several decompositions for Clifford algebra of even dimension under the action of these fundamental operators. 相似文献
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In a recent paper, the authors presented the key ideas involved in their approach to Feynman's operational calculi for systems of not necessarily commuting bounded linear operators acting on a Banach space. The central objects of the theory are the disentangling algebra, a commutative Banach algebra, and the disentangling map which carries this commutative structure into the noncommutative algebra of operators. The study of properties of these disentangling maps will be pursued in this paper with an emphasis on (i) Feynman's formula for disentangling an exponential factor, and (ii) the effect on the disentangling map of ordered supports of some or all of the measures which govern the disentangling. 相似文献
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Sungeun Jung 《中国科学 数学(英文版)》2018,(5)
Given a unilateral forward shift S acting on a complex,separable,infinite dimensional Hilbert space H,an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that{S~(*n)T S~n}is convergent with respect to one of the topologies commonly used in the algebra of bounded linear operators on H.In this paper,we study the asymptotic T_u-Toeplitzness of weighted composition operators on the Hardy space H~2,where u is a nonconstant inner function. 相似文献