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invariant subspaceS AND GENERALIZED FUNCTIONAL SEPARABLE SOLUTIONS TO THE TWO-COMPONENT b-FAMILY SYSTEM

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Acta Mathematica Scientia 2016年第3期36卷 753-764页

作者：闫璐时振华王昊康静 Xingzhi College Xi'an University of Finance and Economics School of Mathematics Northwest University Center for Nonlinear Studies and School of Mathematics Northwest University

invariant subspace method is exploited to obtain exact solutions of the two- component b-family system. It is shown that the two-component b-family system admits the generalized functional separable solutions. Further... 详细信息

关键词： invariant subspace generalized conditional symmetry generalized functional separable solution Camassa-Holm equation two-component b-family system

FAST PARALLELIZABLE METHODS FOR COMPUTING invariant subspaceS OF HERMITIAN MATRICES

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Journal of Computational Mathematics 2007年第5期25卷 583-594页

作者： Zhenyue Zhang Hongyuan Zha Wenlong Ying Department of Mathematics Zhejiang University Hangzhou 310027 China College of Computing Georgia Institute of Technology Atlanta GA 30332 USA

We propose a quadratically convergent algorithm for computing the invariant subspaces of an Hermitian matrix. Each iteration of the algorithm consists of one matrix-matrix multiplication and one QR decomposition. We present an accurate convergence analysis of the algorithm without using the big O notation. We also propose a general framework based on implicit rational transformations which allows us to make connections with several existing algorithms and to derive classes of extensions to our basic algorithm with faster convergence rates. Several numerical examples are given which compare some aspects of the existing algorithms and the new algorithms.

关键词： Eigenvalue invariant subspace Hermitian matrix QR method Parallelizable method.

MULTIPLICATION OPERATORS ON invariant subspaceS OF FUNCTION SPACES

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Acta Mathematica Scientia 2013年第5期33卷 1463-1470页

作者： B.YOUSEFI Sh.KHOSHDEL Y.JAHANSHAHI Department of Mathematics Payame Noor University

Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.

关键词： invariant subspace Hilbert space of analytic functions essential spectrum essential norm Fredholm operator multiplication operator

On Hyperinvariant subspaces of Contraction Operators on a Banach Space Whose Spectrum Contains the Unit Circle

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Acta Mathematica Sinica,English Series 2008年第9期24卷 1471-1474页

作者： Ming Xue LIU Department of Mathematics Guangdong Polytechnic Normal University Guangzhou 510665 P. R. China Department of Mathematics Guangdong Polytechnic Normal University Guangzhou P. R. China

In this paper, we prove that every operator in a class of contraction operators on a Banach space whose spectrum contains the unit circle has a nontrivial hyperinvariant subspace.

关键词： Banach space contraction operator invariant subspace

On Principal invariant subspaces

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Acta Mathematica Sinica,English Series 2015年第10期31卷 1621-1628页

作者： Xiao Ming XU Xiao Chun FANG School of Science Shanghai Institute of Technology Department of Mathematics Tongji University

Let F and G be closed subspaces of the complex Hilbert spaceH, and U and V be closed subspaces of F- and G, respectively. In this paper, using the technique of operator block, we present the necessary and sufficient conditions under which （U, V） is a pair of （strictly, non-degenerate） principal invariant subspaces for （F, G）.

关键词： Hilbert space operator matrix invariant subspace principal invariant subspace

Rank-One Cross Commutators on Backward Shift invariant subspaces on the Bidisk

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Acta Mathematica Sinica,English Series 2009年第5期25卷 693-714页

作者： Kei Ji IZUCHI Kou Hei IZUCHI Department of Mathematics Niigata University Graduate School of Science and Technology Niigata University Department of Mathematics Graduate School of ScienceHokkaido University

For a backward shift invariant subspace N in H^2（Г^2）, the operators Sz and Sw on N are defined by Sz = PNTz｜N and Sw, = PNTw｜N, where PN is the orthogonal projection from L^2（Г^2） onto N. We give a characteri... 详细信息

关键词： backward shift invariant subspace invariant subspace Hardy space cross commutator rank-one operator

On Two Natural Extensions of n-normality

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Acta Mathematica Sinica,English Series 2023年第6期39卷 1147-1152页

作者： Salah MECHERI Faculty of Mathematics and informatics Mohamed El Bachir El Ibrahimi UniversityBordj Bou ArreridjAlgeria

A bounded linear operator T on a complex Hilbert space H is called n-normal if T^(*)T^(n)=T^(n)T^(*).By Fuglede’s theorem T is n-normal if and only if T^(n)is *** k,n∈*** a bounded linear operator T is said to be of typeⅠk-quasi-n-normal if T^(*k){T^(*)T^(n)-T^(n)T^(*)}T^(k)=0,and T is said to be of typeⅡk-quasi-n-normal if T^(*k){T^(*n)T^(n)-T^(n)T^(*n)}T^(k)=0.1-quasi-n-normal is called *** shall show that(1)typeⅠquasi-2-normal and typeⅡquasi-2-normal are different classes;(2)the intersection of the class of typeⅠquasi-2-normal and the class of typeⅡquasi-2-normal is equal to the class of *** also give some examples of type I k-quasi-n-normal and typeⅡ*** also show that Weyl’s theorem holds for this class of operators and every k-quasi-n-normal operator has a non trivial invariant subspace.

关键词： Normal operator n-normal operator invariant subspace

Composition Operators with Universal Translates on S^(2)(D)

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Acta Mathematica Sinica,English Series 2023年第12期39卷 2452-2464页

作者： Kai Kai HAN Yan Yan TANG School of Mathematics and Statistics Hebei University of Economics and BusinessShijiazhuang 050061P.R.China School of Mathematics and Statistics He'nan UniversityKaifeng 475004P.R.China

It is known that the invariant subspace Problem for Hilbert spaces is equivalent to the statement that all minimal non-trivial invariant subspaces for a universal operator are one *** this paper,we characterize all linear fractional composition operators and their adjoints that have universal translates on the space S^(2)(D).Moreover,we characterize all adjoints of linear fractional composition operators that have universal translates on the Hardy space H^(2)(D).In addition,we consider the minimal invariant subspaces of the composition operator Cφa on S^(2)(D),where φa(z)=az+1-a,a ∈(O,1).Finally,some relationships between complex symmetry and universality for bounded linear operators and commuting pairs of operators on a complex separable,infinite dimensional Hilbert space are explored.

关键词： Universal operator composition operator invariant subspace complex symmetry

invariant subspaces and Exact Solutions to the Generalized Strongly Dispersive DGH Equation

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Journal of Applied Mathematics and Physics 2020年第8期8卷 1654-1663页

作者： Xuexia Li Hanze Liu Lina Chang School of Mathematical Sciences Liaocheng University Liaocheng China

In this paper, the invariant subspaces of the generalized strongly dispersive DGH equation are given, and the exact solutions of the strongly dispersive DGH equation are obtained. Firstly, transform nonlinear partial differential Equation (PDE) into ordinary differential Equation (ODE) systems by using the invariant subspace method. Secondly, combining with the dynamical system method, we use the invariant subspaces which have been obtained to construct the exact solutions of the equation. In the end, the figures of the exact solutions are given.

关键词： Generalized Strongly Dispersive DGH Equation Exact Solution invariant subspace