共查询到20条相似文献,搜索用时 78 毫秒
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设A为Banach空间X中一自反代数使得在LatA中O ≠0且X_≠X,则A的每一环自同构¢(环反自同构φ)具有形式¢(A)=TAT^-1(φ(A)=TA^*T^-1),其中T:X→X(T:X^*→X)或为一有界线性双射算子或为一有界共轭线性性双射算子。特别地,¢和φ都是连续的。 相似文献
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自反Banach空间上算子代数的超自反性 总被引:4,自引:0,他引:4
本文引入自发Banach空间上算子代数A的超自反定义,讨论了A超自反的充要条件,超自反常数的估计以及超自反在代数同构下的不变性。 相似文献
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本文首次引入算子集合的C_σ性质和性质的概念,它们与性质C和性质D_σ(1)有一定的关系.两个主要结果是:(1)具有性质C_σ的对偶代数一定是遗传自反的.(2)如果对偶代数所生成的n-自反代数具有性质C_σ,则该对偶代数一定是遗传n-自反的. 相似文献
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算子代数的Cσ性质,C↑~σ性质与自反性 总被引:2,自引:0,他引:2
本文首次引入算子集合的Cσ性质和C↑~σ性质的概念,它们与性质C和性质Dσ(1)有一定的关系:两个主要结果是:(1)具有性质C↑~σ的对偶代数一定是遗传自反的。(2)如果对偶代数所生成的n-自反代数具有性质Cσ,则该对偶代数一定是遗传n-自反的。 相似文献
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《高等学校计算数学学报》2016,(1)
正1引言设X为Banach空间,B(X)表示Banach空间X上有界线性算子的全体.设A∈B(X),则满足方程ABA=A的有界线性算子B∈B(X)称为A的{1}-逆,记作A~-;满足方程ABA=A,BAB=B的有界线性算子B∈B(X)称为A的自反广义逆或A的{1,2}-逆,通常记作A~+.若B∈B(X)满足下列方程 相似文献
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E. Horozov 《Bulletin des Sciences Mathématiques》2002,126(7):605-614
In this paper we give another characterization of the strictly nilpotent elements in the Weyl algebra, which (apart from the polynomials) turn out to be all bispectral operators with polynomial coefficients. This also allows to reformulate in terms of bispectral operators the famous conjecture, that all the endomorphisms of the Weyl algebra are automorphisms (Dixmier, Kirillov, etc). 相似文献
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We study the algebra of operators with the Bergman kernel extended by isometric weighted shift operators. The coefficients of the algebra are assumed to be automorphic with respect to a cyclic parabolic group of fractional-linear transformations of a unit disk and continuous on the Riemann surface of the group. By using an isometric transformation, we obtain a quasiautomorphic matrix operator on the Riemann surface with properties similar to the properties of the Bergman operator. This enables us to construct the algebra of symbols, devise an efficient criterion for the Fredholm property, and calculate the index of the operators of the algebra considered. 相似文献
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本文定义了管范畴上的一些算子,研究了它们的一些性质,给出了循环单列代数的Ringel-Hall代数H(T)的结构常数FML,N的一个计算公式.利用这些算子和这个公式,我们得到了其合成代数C(T)及半单模[l(?)i=1nSi](t∈Z+)在H(T)中的一些中心化子.事实上,它们是H(T)的中心元素,且是H(T)在其合成代数C(T)上代数无关的生成元. 相似文献
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It is shown that a weakly closed operator algebra with the property that each of its invariant subspaces is reducing and which
is either strictly cyclic or has only closed invariant linear manifolds, must be a von Neumann algebra. 相似文献
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V. S. Shul'man 《Mathematical Notes》1974,16(2):739-741
We obtain results concerning the invariant subspaces of strictly cyclic operator algebras. In particular, we show that transitivity of a strictly cyclic algebra implies its strict (and hence even its strong) density.Translated from Matematicheskie Zametki, Vol. 16, No. 2, pp. 253–257, August, 1974. 相似文献
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Monk [1970] extended the notion of the completion of a Boolean algebra to Boolean algebras with operators. Under the assumption
that the operators of such an algebra are completely additive, he showed that the completion of always exists and is unique up to isomorphisms over . Moreover, strictly positive equations are preserved under completions a strictly positive equation that holds in must hold in the completion of . In this paper we extend Monk’s preservation theorem by proving that certain kinds of Sahlqvist equations (as well as some
other types of equations and implications) are preserved under completions. An example is given that shows that arbitrary
Sahlqvist equations need not be preserved.
Received May 3, 1998; accepted in final form October 7, 1998. 相似文献
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S. ter Horst M. Messerschmidt A.C.M. Ran M. Roelands M. Wortel 《Indagationes Mathematicae》2018,29(5):1350-1361
In recent years the coincidence of the operator relations equivalence after extension (EAE) and Schur coupling (SC) was settled for the Hilbert space case. For Banach space operators, it is known that SC implies EAE, but the converse implication is only known for special classes of operators, such as Fredholm operators with index zero and operators that can in norm be approximated by invertible operators. In this paper we prove that the implication EAE SC also holds for inessential Banach space operators. The inessential operators were introduced as a generalization of the compact operators, and include, besides the compact operators, also the strictly singular and strictly co-singular operators; in fact they form the largest ideal such that the invertible elements in the associated quotient algebra coincide with (the equivalence classes of) the Fredholm operators. 相似文献
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Domingo A. Herrero 《Integral Equations and Operator Theory》1987,10(2):297-303
The title refers to an empty class of operators. Moreover, if T is a triangular Banach space operator, then either T is algebraic and the double commutant has infinite strict multiplicity, or T is not algebraic and the commutant has infinite strict multiplicity. A rationally strictly cyclic, but not strictly cyclic, operator cannot have finite strict multiplicity.This research was partially supported by a Grant of the National Science Foundation. 相似文献
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For every Ore extension we construct a chain complex giving its Hochschild homology. As an application we compute the Hochschild and cyclic homology of an arbitrary multiparametric affine space and the Hochschild homology of the algebra of differential operators over this space, in the generic case. 相似文献
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We develop intrinsic tools for computing the periodic Hopf cyclic cohomology of Hopf algebras related to transverse symmetry in codimension 1. Besides the Hopf algebra found by Connes and the first author in their work on the local index formula for transversely hypoelliptic operators on foliations, this family includes its ‘Schwarzian’ quotient, on which the Rankin-Cohen universal deformation formula is based, the extended Connes-Kreimer Hopf algebra related to renormalization of divergences in QFT, as well as a series of cyclic coverings of these Hopf algebras, motivated by the treatment of transverse symmetry for non-orientable foliations.The method for calculating their Hopf cyclic cohomology is based on two computational devices, which work in tandem and complement each other: one is a spectral sequence for bicrossed product Hopf algebras and the other a Cartan-type homotopy formula in Hopf cyclic cohomology. 相似文献