Krein空间上J-正常算子的可定化性

对于Krein空间上J-正常算子 的各种可定化性进行了研究. 利用可定化J-正常算子的谱函数, 给出了临界线的概念, 得到了可定化的J-正常算子成为强可定化算子和一致可定化算子的充要条件.     

Simultaneously Definitizable and Spectralizable Operators in Krein Space

We study the spectral properties of a self–adjoint operator in Krein space such that one of its natural powers is J–non–negative and some other power is a spectral operator in the Dunford sense.     

On Strongly Stable Normal Operators in Krein Spaces

We give a necessary and sufficient condition for strong stability of bounded normal operators in Krein spaces. A similar result was obtained for unitary operators by M. G. Krein [1], and for selfadjoint operators by H. Langer [2], [3].     

Normal Extensions of Operators to Krein Spaces

In this paper, it is proved that every bounded linear operator on a Hilbert space has a normal extension to a Krein space. Two criteria for J-subnormality are given. In particular, in order that T be subnormal, it suffices that exp(-\bar \Lambda T^*)exp(\Lambda T) be a positive definite operator function on a bounded infinite subset of complex plane. This improves the condition of Bram [4]. Also it is proved that the local spectral subspaces are closed for J-subnormal operators.     

Analysis of Spectral Points of the Operators T [*] T and TT [*] in a Krein Space

Spectra and sets of regular and singular critical points of definitizable operators of the form T ^[*] T and TT ^[*] in a Krein space are compared. The relation between the Jordan chains of the above operators (corresponding to the same eigenvalue) is shown.      

A Variational Principle in Krein Space II

Let A be a self-adjoint operator in a Krein space Under certain natural assumptions, it is shown precisely which real eigenvalues of A can be given a max-inf characterization generalizing the usual one in Hilbert space. This result unifies several approaches in the recent literature.     

Boundary Relations and Generalized Resolvents of Symmetric Operators in Krein Spaces

The classical Krein-Naimark formula establishes a one-to-one correspondence between the generalized resolvents of a closed symmetric operator in a Hilbert space and the class of Nevanlinna families in a parameter space. Recently it was shown by V.A. Derkach, S. Hassi, M.M. Malamud and H.S.V. de Snoo that these parameter families can be interpreted as so-called Weyl families of boundary relations, and a new proof of the Krein-Naimark formula in the Hilbert space setting was given with the help of a coupling method. The main objective of this paper is to adapt the notion of boundary relations and their Weyl families to the Krein space case and to prove some variants of the Krein-Naimark formula in an indefinite setting.      

Spectral Theorem for Definitizable Normal Linear Operators on Krein Spaces

In the present note a spectral theorem for normal definitizable linear operators on Krein spaces is derived by developing a functional calculus \({\phi \mapsto \phi(N)}\) which is the proper analogue of \({\phi \mapsto \int \phi \, dE}\) in the Hilbert space situation. This paper is the first systematical study of definitizable normal operators on Krein spaces.     

The Krein String and Characteristic Functions of Maximal Dissipative Operators

Theory of the Krein string is considered in the framework of a continual analog of the theory of unitary operator nodes. On this basis, a generalization of the M. G. Krein-A. A. Nudelman result on the completeness of the string operator is obtained. Bibliography: 28 titles.     

Orlicz空间上的乘法算子

函数空间上的乘法算子是包含许多重要算子的算子类,该文主要研究Orlicz空间上乘法算子的一系列重要性质,包括有界性、紧性、Fredholm性质以及谱的计算等     

Singular Rank One Perturbations of Self-Adjoint Operators and Krein Theory of Self-Adjoint Extensions

Gesztesy and Simon recently have proven the existence of the strong resolvent limit A_, for A_, = A + (·), where A is a self-adjoint positive operator, being the A-scale). In the present note it is remarked that the operator A_, also appears directly as the Friedrichs extension of the symmetric operator :=A \{f (A)| f,=0\}. It is also shown that Krein's resolvents formula: (A_{_b,}-z)^-1 =(A-z)^-1+ (·, ) _z, with b=b-(1+z) (_z,_-1),_z= (A-z)^-1 defines a self-adjoint operator A_b, for each and b R¹. Moreover it is proven that for any sequence _n which goes to in there exists a sequence _n0 such that A_b, in the strong resolvent sense.     

On Finite Rank Perturbations of Selfadjoint Operators in Krein Spaces and Eigenvalues in Spectral Gaps

It is shown that the finiteness of eigenvalues in a spectral gap of a definitizable or locally definitizable selfadjoint operator in a Krein space is preserved under finite rank perturbations. This results is applied to a class of singular Sturm–Liouville operators with an indefinite weight function.     

Increasing Monotone Operators in Banach Space

An operator mapping a separable reflexive Banach space X into the dual space X is called increasing if as . Necessary and sufficient conditions for the superposition operators to be increasing are obtained. The relationship between the increasing and coercive properties of monotone partial differential operators is studied. Additional conditions are imposed that imply the existence of a solution for the equation with an increasing operator A.     

Dirichlet空间上的紧算子

若S是Dirichlet空间上有限个Toeplitz算子乘积的有限和, S为紧算子的充要条件是: 当z→∂D时, S的Berezin型变换收敛到0; 若S是Dirichlet空间上Hankel算子, S为紧算子的充要条件是: 当z→ D时, S作用在类再生核上按范数收敛到0.     

The Generalized p-Normal Operators and p-Hyponormal Operators on Banach Space

In this paper, the authors discuss the generalized p-normal and p-hyponormal operators on Banach space. Some results in this paper are the generalization of Sen’s results on generalized p-selfadjoint operator and some open questions of Sen’s are answered. For the generalized p-normal operator’s, the following formulae are obtained: r(T)=||T||,||(T-\Lambda I)^-1||=\frac{1}{dist(\Lambda,\sigma(T))}.     

从Bergman空间到Bloch空间的叠加算子

研究从Bergman空间到Bloch空间的叠加算子.从函数空间的性质出发,利用不同维数的函数空间之间的关系,讨论叠加算子,把单变量有关叠加算子的结果推广到多变量,得到了与单变量一致的结果,从而刻画了从Bergman空间到Bloch空间的叠加算子的特征,得到了从Bergman空间到Bloch空间的叠加算子的充要条件.     

Banach空间上的强混合算子

1999年,L．B．Gonzalez 证明了任意无限维可分 Banach 空间上存在拓扑传递的有界线性算子．这个结果肯定地回答了 S．Rolewicz 提出的问题．本文证明了由 L．B．Gonzalez 所给出的算子实际上是强混合的,同时,对加权移位算子的混合性利用权序列进行了刻划并指出任意无限维可分 Hilbert 空间上存在弱混合而非强混合的有界线性算子．     

Banach空间上的强混合算子

1999年,L.B.Gonzalez证明了任意无限维可分Banach空间上存在拓扑传递的有界线性算子.这个结果肯定地回答了S.Rolewicz提出的问题.本文证明了由L.B.Gonzalez所给出的算子实际上是强混合的,同时,对加权移位算子的混合性利用权序列进行了刻划并指出任意无限维可分Hilbert空间上存在弱混合而非强混合的有界线性算子.     

Toeplitz Operators on the Dirichlet Space

In this paper a decomposition of Sobolev space is obtained. Then we prove that a Toeplitz operator on the Dirichlet space is compact only when it is the zero operator. For two Toeplitz operators on the Dirichlet space, we obtain the conditions for that they commute, their product is a Toeplitz operator, and their commutator or semi-commutator has finite rank, respectively.