算子的拟相似与(Q)类算子

本文引进定义于L(H)上的集值函数β(S)和(Q)类算子(指本质谱含于其一切拟相似算子的本质谱的算子),用β(S)刻划 (Q)类算子的特征;证明(Q)类算子范围广泛,次可分解算子(包括次标量算子,M-亚正常算子,半亚正常算子等等)是其中的一部分;(Q)类算子在L(H)中稠密.     

Averaged Wave Operators and Complex-symmetric Operators

We study the behaviour of sequences \(U_2^n X U_1^{-n}\), where \(U_1, U_2\) are unitary operators, whose spectral measures are singular with respect to the Lebesgue measure, and the commutator \(XU_1-U_2X\) is small in a sense. The conjecture about the weak averaged convergence of the difference \(U_2^n X U_1^{-n}-U_2^{-n} X U_1^n\) to the zero operator is discussed and its connection with complex-symmetric operators is established in a general situation. For a model case where \(U_1=U_2\) is the unitary operator of multiplication by z on \(L^2(\mu )\), sufficient conditions for the convergence as in the Conjecture are given in terms of kernels of integral operators.     

Continuity of Operators Intertwining with Convolution Operators

Let G be a locally compact abelian group, let μ be a bounded complex-valued Borel measure on G, and let T_μ be the corresponding convolution operator on L¹(G). Let X be a Banach space and let S be a continuous linear operator on X. Then we show that every linear operator Φ: X→L¹(G) such that ΦS=T_μΦ is continuous if and only if the pair (S,T_μ) has no critical eigenvalue.     

Pseudodifferential Operators Associated with a Semigroup of Operators

Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifolds, fractals, graphs etc.). Boundedness on L ^p for pseudodifferential operators of order 0 is proved. We mainly focus on symbols belonging to the class $S^{0}_{1,\delta}$ for δ∈[0,1). For the limit class $S^{0}_{1,1}$ , we describe some results by restricting our attention to the case of a sub-Laplacian operator on a Riemannian manifold.     

单调算子和强制算子的相补问题

讨论了单调算子和强制算子的相补问题，给出了解的存在性定理。并进一步证明了严格单调算子的解的唯一定理。     

可亚正规化的算子

最近,Ky Fan在[1]中就有限维希尔伯特空间引进了所谓可正规化算子的概念,考察了这类算子的一系列特征,其实在[1]中给出的可正规化算子的概念推广到无限维的Hilbert空间时,所列出的绝大部分特征也是成立的,希氏空间H上的线性有界算子T称为可正规化的,是指存在H上的可逆算子S,使S~*TS是正规算子。     

Sampling of Operators

Sampling and reconstruction of functions is a fundamental tool in science. We develop an analogous sampling theory for operators whose Kohn-Nirenberg symbols are bandlimited. We prove sampling theorems for in this sense bandlimited operators and show that our results generalize both, the classical sampling theorem, and the fact that a time-invariant operator is fully determined by its impulse response.     

Intertwining Operators Associated to a Family of Differential-Reflection Operators

Mediterranean Journal of Mathematics - We introduce a family of differential-reflection operators $${\Lambda_{A, \varepsilon}}$$ acting on smooth functions defined on $${{\mathbb R}}$$ . Here, A is...     

S-Storage Operators

In 1990, J. L. Krivine introduced the notion of storage operator to simulate, for Church integers, the “call by value” in a context of a “call by name” strategy. In the present paper we define for every λ-term S which realizes the successor function on Church integers the notion of S-storage operator. We prove that every storage operator is an S-storage operator. But the converse is not always true.     

p-Dirac Operators

We introduce non-linear Dirac operators in associated to the p-harmonic equation and we extend to other contexts including spin manifolds and the sphere. This paper is dedicated to the memory of Jarolim Bureš Received: October, 2007. Accepted: February, 2008.     

Spectralizable Operators

We introduce the notion of spectralizable operators. A closed operator A in a Hilbert space is called spectralizable if there exists a non-constant polynomial p such that the operator p(A) is a scalar spectral operator in the sense of Dunford. We show that such operators belongs to the class of generalized spectral operators and give some examples where spectralizable operators occur naturally. Vladimir Strauss gratefully acknowledges support by DFG, Grant No. TR 903/3-1.     

Spectral Doubling of Normal Operators and Connections with Antiunitary Operators

Equations such as AB = B ^T A have been studied in the finite dimensional setting in (Linear Algebra Appl 369:279–294, 2003). These equations have implications for the spectrum of B, when A is normal. Our aim is to generalize these results to an infinite dimensional setting. In this case it is natural to use JB*J for some conjugation operator J in place of B ^T . Our main result is a spectral pairing theorem for a bounded normal operator B which is applied to the study of the equation KB = B*K for K an antiunitary operator. In particular, using conjugation operators, we generalize the notion of Hamiltonian operator and skew-Hamiltonian operator in a natural way, derive some of their properties, and give a characterization of certain operators B for which AB = (JB*J)A and BA = A(JB*J) and also those B with KB = B*K for certain antiunitary operators K.     

亚超循环算子与可逆算子的亚超循环性

设X为无限维可分的Banach空间,T是X上的有界线性算子.利用轨道C·Orb(x,T)的d稠密性给出了T是亚超循环算子的充分条件.此外,还考虑可逆的亚超循环算子T并从循环向量的角度刻画了T和T~(-1)的亚超循环性.     

Conditions for Admissibility of Observation Operators and Boundedness of Hankel Operators

We derive new necessary and sufficient conditions for admissibility of observation operators for certain C ₀-semigroups. We also prove a new sufficient criterion for admissibility for observation operators with infinite-dimensional output space on contraction semigroups. If the contraction semigroup is completely non-unitary and its co-generator has finite defect indices, then this criterion is also necessary. In the case of the right shift semigroup on L ²(0,), these conditions translate into conditions for the boundedness of Hankel operators.     

(NCI)算子与(NFI)算子

引入两类与不变子空间密切相关的算子,即(NCI)算子与(NFI)算子.考虑这两类算子的性质,例如存在性,相似不变性,以及与强不可约算子的关系等.并在可分Banach空间上讨论谱为单点集{0}的算子能否小紧摄动成为(NFI)算子.     

关于线性算子的概率范数与算子空间

由于满足(PN-5)条件的PN空间(E,F)就是MangerPN空间(E,F,min),因此,肖建中等给出的关于PN空间上线性算子概率范数的结果有较大的局限性.本文中,在较一般的MengerPN空间上研究有关线性算子的概率范数和算子空间的问题,改进和推广了肖建中等的结果.     

q-deformed Circular Operators

In this paper, q-deformed circularity of an operator in a Hilbert space is introduced and investigated. In particular, the q-deformed circularity of a weighted shift is characterized by an integer, which is uniquely determined by the operator. It is shown that that the spectrum of a q-deformed circular weighted shift is the whole complex plane.     

Representable Monotone Operators and Limits of Sequences of Maximal Monotone Operators

We show that the lower limit of a sequence of maximal monotone operators on a reflexive Banach space is a representable monotone operator. As a consequence, we obtain that the variational sum of maximal monotone operators and the variational composition of a maximal monotone operator with a linear continuous operator are both representable monotone operators.     

算子的本性相似

对作用于一复可分无穷维Hilbet空间(？)上的两个有界线性算子T,S,它 们本性相似和π(T),π(S)(T,S在Calkin代数中的象)相似是否等价？这是有趣的问 题.本文引入一个算子类ES((？)),并证明了对ES((？))中的算子,上面提到的两种相 似性是等价的. 此外,还证明了ES((？))在B((?))中按照算子范数拓扑稠密.     

Conditions of Spectrum Localization for Operators not Close to Self-Adjoint Operators

The Keldysh theorem is generalized to an arbitrary closed operator that is not necessarily close to self-adjoint operators and has a resolvent of Schatten–von Neumann class S _p . Based on this theorem, conditions of spectrum localization are obtained for certain classes of non-self-adjoint differential operators.