共查询到20条相似文献,搜索用时 78 毫秒
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类似与标型谱算子,U-标算子是否拟仿射相似于自伴算子是一“公开问题”.尽管对具纯离散谱的U-标算子答案是肯定的,但一般情况下并不成立.本文继续探讨这一问题,证明了U-标算子在一强范数拓扑意义下是Hermite算子,或者说U-标算子拟仿射相似于Hermite算子,并给出U-标算子是标型谱算子的充要条件. 相似文献
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本文定义了非线性算子的Lip数,它从数值上刻画了在强等价距离意义下非线性算子的最小Lipschitz常数.基于所引进的Lip数,我们证明了线性算子Neumann引理及扰动引理的非线性推广.我们也给出了Lip数的两个极有意义的估值定理. 相似文献
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非线性Lipschitz算子的定量性质(Ⅰ)—Lip数 总被引:10,自引:0,他引:10
本文定义了非线性算子的Lip数,它从数值上刻画了在强等价距离意义下非线性算子的最小Lipschitz常数。 相似文献
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本文通过引入若干Lipschitz对偶概念,将非线性Lipschitz算子半群对偶映射到Lipschitz对偶空间中,使其转化为线性算子半群。该线性算子半群被证明是一个C_0~*-半群,因而是某个C_0-半群的对偶半群。从而证明了,在等距意义下,一个非线性Lipschitz算子半群可以延拓为一个C_0-半群。基于这些结论,本文给出了一系列全新的非线性Lipschitz算子半群的表示公式。 相似文献
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研究非线性算子方程的近似求解方法.首先对通常的求解非线性方程加速迭代格式进行推广,得到高阶收敛速度的加速迭代格式,最后把这种加速迭代格式推广到非线性算子方程的求解中去,利用非线性算子的渐进展开,证明了这种加速格式具有三阶的收敛速度. 相似文献
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We introduce a class G of completely continuous operators and prove theorems on the spectral structure of these operators. In particular, operators of this class are similar to model operators in de Branges spaces. 相似文献
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We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem. 相似文献
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Chung-Chou Jiang 《Linear algebra and its applications》2009,430(1):553-749
In this paper, we study the problem of characterizing the bounded linear operators on a Hilbert space that admit a factorization as a product of two Hermitian operators. It is shown that a normal operator can be decomposed as a product of two Hermitian operators if and only if it is similar to its adjoint. Some partial results about hyponormal operators are obtained. 相似文献
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Normal operators similar to irreducible operators 总被引:1,自引:0,他引:1
A complete characterization of normal operators which are similar to irreducible operators and some related results are given. 相似文献
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We investigate pairs of commuting Foias-Williams/Peller type operators acting on vector-valued weighted Bergman spaces. We prove that a commuting pair of such operators is jointly polynomially bounded if and only if it is similar to a pair of contractions, if and only if both operators are polynomially bounded. 相似文献
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Ts. Bayasgalan 《Acta Mathematica Hungarica》1998,81(3):275-278
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]. 相似文献