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An algebraic invariant for Jordan automorphisms on B(H):The set of idempotents

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Science china mathematics 2005年第12期48卷 1585-1596页

作者： CUI Jianlian & HOU Jinchuan department of Mathematical Science, Tsinghua university, Beijing 100084, china department of Applied mathematics, Taiyuan university of Technology, Taiyuan 030024, china department of mathematics, shanxi teachers university, linfen 041004, china department of Mathematical Science Tsinghua University Beijing 100084 China department of Applied mathematics Taiyuan University of Technology Taiyuan 030024 China department of mathematics Shanxi Teachers University Linfen 041004 China

Let H be an infinite dimensional complex Hilbert space. Denote by B(H) the algebra of all bounded linear operators on H, and by I(H) the set of all idempo-tents in B(H). Suppose that Φ is a surjective map from B(H) onto itself. If for every λ ∈ {-1,1,2,3,1/2,1/3} and A, B ∈ B(H), A - λB ∈ I(H) (?) Φ(A) - λΦ(B) ∈ I(H), then Φ is a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that Φ(A) = TAT-1 for all A ∈ B(H), or Φ(A) = TA*T-1 for all A ∈ B(H); if, in addition, A-iB ∈ I(H) (?) Φ(A) -ιΦ(B) ∈ I(H), here ι is the imaginary unit, then Φ is either an automorphism or an anti-automorphism.

关键词： Hilbert space operators,Jordan automorphisms,idempotents.

CHARACTERIZATIONS OF JORDAN (?)-SKEW MULTIPLICATIVE MAPS ON OPERATOR ALGEBRAS OF INDEFINITE INNER PRODUCT SPACES

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Chinese Annals of mathematics,Series B 2005年第4期 82-95页

作者： AN RUNLING HOU JINCHUAN department of mathematics, shanxi university, Taiyuan 030000, china. department of mathematics, shanxi teachers university, linfen 041004, shanxi, china.

Let H and K be indefinite inner product spaces. This paper shows that a bijective map φ:B(H)→B(K) satisfies φ(AB+ + B+A) =φ(A)φ(5)+ +φ(B)+φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = cU AU+ for all A or φ(A) = cUA+U+ for all A; φsatisfies φ(AB+A) = φ(A)φ(B)+φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = UAV for all A or φ(A) = UA+V for all A, where A+ denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with U+U = c-1I and V+V = cI for some nonzero real number c.

关键词： Indefinite inner product spaces (?)-Automorphisms Jordan product

THE SPECTRAL COMPLETION OF A CLASS OF OPERATOR PARTIAL MATRICES

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Systems Science and Mathematical Sciences 2000年第4期13卷 358-365页

作者： CUI Jianlian (Institute of mathematics, Chinese Academy of Sciences, Beijing 100080, china) HOU Jinchuan GAO Mingchu (department of mathematics, shanxi teachers university, linfen 041004, china) 中科院数学所北京 100080 山西师范大学数学系山西临汾 041004 山西师范大学数学系山西临汾

A sufficient and necessary condition is given for the operator partial matrix () to have a completion T = () such that σ(T) Ω with X and Y being compact operators, where Ω is a given open set containing zero in the complex plane with every component being simply connected. This result is also used to discuss the power stabilizability of the discrete time infinite dimensional systems.

关键词： Operator partial matrix spectrum linear system.

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算子张量积及C_2上的初等算子

数学学报（中文版） 1995年第4期38卷 467-474页

作者：侯晋川山西师范大学数学系

本文给出了形如的张量积算子成为自伴算子，Ｃ＿ｐ类算子，有限秩算子及一秩算子的充分必要条件，特别，作为应用，得到Ｈｉｌｂｅｒｔ－Ｓｃｈｍｉｄｔ类Ｃ＿２（Ｈ）上初等算子成为自伴算子，Ｃ＿ｐ类算子的充分必要条件．

关键词：算子张量积 Cp类算子初等算子自伴算子

ARC-TRANSITIVE CUBIC GRAPHS OF ORDER 4_p

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Chinese Annals of mathematics,Series B 2004年第4期25卷 545-554页

作者： XUMINGYAO ZHANGQINHAI ZHOUJINXIN SchoolofmathematicsandComputerSciences ShanxiTeachersUniversityLinfen041004ShanxiChina SchoolofmathematicsandComputerSciences ShanxiTeachersUniversityLinfen041004ShanxiChina.

In this paper, a complete classification of arc-transitive cubic graphs of order 4p is given.

关键词： Arc-transitive graph Cubic s-regular graph Coverings of a graph

C-Wellposedness of the Complete Second Order Abstract Cauchy Problem and Applications

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Acta Mathematica Sinica,English Series 1999年第4期15卷 535-548页

作者： Mingchu Gao department of mathematics,shanxi teachers university,linfen 041004,P.R.china E-mail:mcgao@*** department of mathematics Shanxi Teachers University Linfen P. R. China

In this paper,we first give a sufficient and necessary condition for M= to generate an exponentially bounded =-semigroup and discuss its relations to the C-wellposedness of the complete second order abstract Cauchy problem （（ACP2） for short） in some *** we use these results and those in [1] to discuss the C-（exponential） wellposedness of a kind of （ACP2） with application backgrounds,and develop the results in [2].

关键词： Abstract Cauchy problem C-semigroup C-wellposedness

A Characterization of Homomorphisms Between Banach Algebras

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Acta Mathematicae Applicatae Sinica 2004年第4期 761-768页

作者： Jian Lian CUI department of Mathematical Sciences,Tsinghua university,Beijing 100084 P.R.china and department of mathematics,shanxi teachers university,linfen 041004,P.R.china Jin Chuan HOU department of mathematics,shanxi teachers university,linfen 041004,P.R.china and department of mathematics,shanxi university,Taiyuan 030000,P.R.china

We show that every unital invertibility preserving linear map from a yon Neumann algebraonto a semi-simple Banach algebra is a Jordan homomorphism;this gives an affirmative answer to aproblem of Kaplansky for all von Neumann *** a unital linear map Φ from a semi-simplecomplex Banach algebra onto another,we also show that the following statements are equivalent:(1)Φ is an homomorphism;(2)Φ is completely invertibihty preserving;(3)Φ is 2-invertibility preserving.

关键词： Banach algebras Homomorphisms Jordan homomorphisms

Structures and stability of (HAlNH)_n(n=1-15)

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Chinese Science Bulletin 2001年第18期46卷 1507-1514页

作者： WU Haishun, ZHANG Congjie, XU Xiaohong, ZHANG Fuqiang & ZHANG Qianerdepartment of Chemistry, shanxi Normal university, linfen 041004, china department of Chemistry, Xiamen university, Xiamen 361005, china department of Chemistry Shanxi Normal University Linfen China department of Chemistry Xiamen University Xiamen China

The geometries, electronic states, vibrational spectra and thermodynamic properties for (HAINH)n clusters with n=1-15 have been investigated using the ab initio DFT/B3LYP method with basis sets 6-31G* and their ground state structures obtained. Comparison of the (HAINH)n with (A1N)n clusters shows that the skeletons of (HAINH)n consist of four-membered and six-membered rings made of Al-N bonds, and either Al or N atom forms four bonds in which three ones are Al-N bonds and the rest is Al-H or N-H bond. The number of Al-N bonds of (HAINH)n is equal to that of (AlN)n. The magic number regularity of (HAINH)n is n =2, 4, 6, 8, etc., all of which are even numbers.

关键词： DFT method (HAINH)n cluster structure stability.

On quasi-convex mappings of order α in the unit ball of a complex Banach space

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Science china mathematics 2006年第11期49卷 1451-1457页

作者： LIU Taishun & XU Qinghua department of mathematics, Huzhou teachers College, Huzhou, 313000, china department of mathematics, Jiangxi Normal university, Nanchang, 330022, china department of mathematics Huzhou Teachers College Huzhou China department of mathematics Jiangxi Normal University Nanchang China

In this paper, a class of biholomorphic mappings named quasi-convex mapping of order a in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order a defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively.

关键词： coefficient estimation the homogeneous expansion quasi-convex mapping quasi-convex mapping of order a.