多圆盘的加权Bergman空间上的不变子空间和约化子空间

本文主要研究多圆盘的加权Bergman 空间上的不变子空间和约化子空间, 给出了某些解析Toeplitz 算子的极小约化子空间的完全刻画, 以及一类解析Toeplitz 算子Tzi (1≤i≤n) 的不变子空间的Beurling 型定理.     

Efficient Computation of Analytic Bases in Evans Function Analysis of Large Systems

In Evans function computations of the spectra of asymptotically constant-coefficient linearized operators of large systems, a problem that becomes important is the efficient computation of global analytically varying bases for invariant subspaces of the limiting coefficient matrices. In the case that the invariant subspace is spectrally separated from its complementary invariant subspace, we propose an efficient numerical implementation of a standard projection-based algorithm of Kato, for which the key step is the solution of an associated Sylvester problem. This may be recognized as the analytic cousin of a C ^k algorithm developed by Dieci and collaborators based on orthogonal projection rather than eigenprojection as in our case. For a one-dimensional subspace, it reduces essentially to an algorithm of Bridges, Derks and Gottwald based on path-finding and continuation methods.     

Invariant subspaces of operator algebras

The survey is devoted to a circle of problems, grouped around one of the oldest problems of functional analysis, namely the invariant subspace problem. It is shown that the investigation of the algebraic and analytic properties of families of operators touches upon the question of the structure of their invariant subspaces.Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 26, pp. 65–145, 1988.     

On a Class of Operators of Finite Type

This paper studies some class of pure operators A with finite rank self-commutators satisfying the condition that there is a finite dimensional subspace containing the image of the self-commutator and invariant with respect to A*. Besides, in this class the spectrum of operator A is covered by the projection of a union of quadrature domains in some Riemann surfaces. In this paper the analytic model, the mosaic and some kernel related to the eigenfunctions are introduced which are the analogue of those objects in the theory of subnormal operators.     

On the semi-hyponormal n-tuple of operators

The theory of singular integral model and trace formula is extended to the context of hyponormal or semi-hyponormal n-tuple of operators. The spectrum of noncommutative n-tuple of operators is examined.     

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).     

一类不变的Hankel算子

对于Ｌ^a,2（Ｄ）的两类Ｍｏｅｂｉｕｓ不变子空间Ａ_l^a,2（Ｄ）与Ａ_l^-a,2（Ｄ）,定义了对解析的记号函数ｂ（ｚ）的大的和小的Ｈａｎｋｅｌ算子Ｈ_b^ll′与ｈ_b^ll′,研究了它们的有界性、紧性及其Ｓｃｈａｔｔｅｎ－ｖｏｎ Ｎｅｕｍａｎｎ类的Ｓ_P估计．性质。     

Invariant subspaces of positive strictly singular operators on Banach lattices

It is shown that every positive strictly singular operator T on a Banach lattice satisfying certain conditions is AM-compact and has invariant subspaces. Moreover, every positive operator commuting with T has an invariant subspace. It is also proved that on such spaces the product of a disjointly strictly singular and a regular AM-compact operator is strictly singular. Finally, we prove that on these spaces the known invariant subspace results for compact-friendly operators can be extended to strictly singular-friendly operators.     

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。     

A characteristic operator function for the class of n-hypercontractions

We consider a class of bounded linear operators on Hilbert space called n-hypercontractions which relates naturally to adjoint shift operators on certain vector-valued standard weighted Bergman spaces on the unit disc. In the context of n-hypercontractions in the class C0⋅ we introduce a counterpart to the so-called characteristic operator function for a contraction operator. This generalized characteristic operator function Wn,T is an operator-valued analytic function in the unit disc whose values are operators between two Hilbert spaces of defect type. Using an operator-valued function of the form Wn,T, we parametrize the wandering subspace for a general shift invariant subspace of the corresponding vector-valued standard weighted Bergman space. The operator-valued analytic function Wn,T is shown to act as a contractive multiplier from the Hardy space into the associated standard weighted Bergman space.     

Strongly Invariant Subspaces of Nonautonomous Linear Periodic Systems and Solutions Whose Period Is Incommensurable with the Period of the System Itself

We introduce the notions of quasi-invariant and strongly invariant subspaces of a one-parameter family of linear operators acting on a finite-dimensional vector space. The geometric meaning of these notions is that the restrictions of all operators of the family to a quasiinvariant subspace coincide and that the restrictions to a strongly invariant subspace are, in addition, an endomorphism of that subspace. These notions are used to reduce the well-known problem on Ω-periodic solutions of an ω-periodic linear differential system with incommensurable Ω and ω to the algebraic problem on the eigenvalues and eigenvectors of some matrix constructed from the right-hand side of the system.     

Invariant Subspaces of Operator Lie Algebras and the Theory of K-Algebras

It is proved that if a Lie algebra of compact operators contains a nonzero ideal consisting of quasinilpotent operators then this Lie algebra has a nontrivial invariant subspace. Some applications of this result to lattices of invariant subspaces for families of compact operators and to structures of ideals of Banach Lie algebras with compact adjoint action are given.     

加权Bergman空间中的不变子空间上的根算子

In this paper, for an invariant subspace I of the weighted Bergman space, the weighted root operator is defined. We study the weighted root operator and obtain its fundamental properties when the invariant subspace I has finite index. Furthermore, we give some examples of the root operator and estimate ranks of the operators.     

Analytically invariant spectral resolvents of closed operators

The concept of analytically invariant subspace, in the framework of spectral resolvents, is extended to unbounded closed operators. One obtains necessary and sufficient conditions for a spectral resolvent to be analytically invariant. An application, concerning a strong type of spectral decomposition for closed operators with the spectra on the real line, concludes this study.     

Invariant Maximal Positive Subspaces and Polar Decompositions

It is proved that invertible operators on a Krein space which have an invariant maximal uniformly positive subspace and map its orthogonal complement into a nonnegative subspace allow polar decompositions with additional spectral properties. As a corollary, several classes of Krein space operators are shown to allow polar decompositions. An example in a finite dimensional Krein space shows that there exist dissipative operators that do not allow polar decompositions.     

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⊥ =∞     

Invariant subspaces of direct sums of finite convolution operators

Integral Equations and Operator Theory - In general, a direct sum of finite convolution operators has a very complicated invariant subspace structure. In some cases, however, the invariant...     

Pontriagin空间上算子的交换性

证明了:当Pontrjagin空间上的正规算子A没有零性不变子空间时,Putnam- Fuglede定理成立;当正规算子A有零性不变子空问时,通过构造反例说明此时Putnam- Fuglede定理不成立,并对Π1空间上算子相关的交换性条件进行了讨论,得到了Π1空间上算子代数的二次交换定理．     

一类Hankel算子与Toeplitz算子的Sp性质

对于L~(α,2)(D))的两类Moebius不变子空间A~(α,2)(D)和A~(β,2)(D),我们定义了它们之间的Toeplitz算子T_f~s与其乘积空间上的Hankel算子H_f~r,并且研究了它们的有界性、紧性及Schatten-von Neumann性质。     

次可分解算子的不变子空间格的丰富性

证明了一类次可分解算子的不变子空间格是丰富的,并举例说明存在Hilbert空间上的有界线性算子T,它有无穷多个不变子空间,但是它的不变子空间格Lat(T)不丰富．