跳到主要內容

簡易檢索 / 詳目顯示

回結果列表
研究生： 陳正忠
Zhen-Zhong Chen
論文名稱： 關於超循環算子的一些基本性質
指導教授： 蕭勝彥
Sen-Yen Shaw
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
畢業學年度： 88
語文別： 中文
論文頁數： 30
中文關鍵詞： 超循環算子
相關次數： 點閱：6  下載：0 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報


    • Hypercyclic operators的定義可以說是從Devany chaos operator定義中的一個性質發展出來的，也是最常被提到一種chaos system，其年代可追溯到西元1969年。
    研究的方法以不同的觀點來觀察hypercyclic operators的定義，並以循序漸進的方法來描述hypercyclic operators的形式。從metric space上的mappings，到Banach space上的operators，再到Banach space上的 linear operators，一直到Banach space上的bounded linear operator，然後在和一些強連續半群下的已知結果互相比較。
    最後，在Banach space上的bounded linear operators有比較明顯的可判別結果。在Kato收斂意義下，不見得保有原來hypercyclic的性質但是在某些條件下則會成立。Hereditary hypercyclic operators可得到更好的結果。然後，從第一節和第五節中可看出它們有一些近似的結果。

    Contents Section 0 .Introduction.....................................1 Section 1. Hypercyclic Operators.............................3 Section 2. The Collection of Hypercyclic Vectors.............11 Section 3. Approximation In The Sense Of Kato................16 Section 4. Hereditarily Hypercyclic Operators................20 Section 5. Hypercyclic Semigroups............................25 References...................................................29

    [1] S. I. Ansari, Hypercyclic and cyclic vectors,J. Funct. Anal. 128 (1995), 374-383.
    [2] G. Godefroy and J. H. Shapiro, Operators with dense, invariant, cyclic vector manifolds. J. Funct. Anal. 98(1991), 229-269.
    [3] C. J. Read, The invariant subspace problem for a class of Banach spaces. II. Hypercyclic operators, Israel J. Math 63(1988), 1-40.
    [4] R. deLaubenfels, H. Emamirad and V. Protopopescu, Linear chaos and approximation.
    [5] J. Banks, J. Brooks, G.Cairns, G. Davis, and P. Stacey, On Devaney''s definition of chaos, Amer. Math. Monthly 99(1992), 332-334.
    [6] T. Ushijima, Approximation theory for semigroups of linear operators, Japan J. Math. 1 (1975), 185-224.
    [7] K.-G. Grosse-Erdmann, Universal families and hypercyclic operators. Bull. Amer. Math. Soc. 36(1999), 345-381.
    [8] F. Leaon-Saavedra and A. Montes-Rodriguez. Linear structure of hypercyclic vectors, J. Funct. Anal. 148(1997), 524-545.
    [9] H. Salas, A hypercyclic operator whose adjoint is also hypercyclic, Proc. Amer. Math. Soc. 112(1991), 765-770.
    [10] J. Bes, Hereditarily hypercyclic operators ,J.Funct.Anal. 167 (1999), 94-112.
    [11] A. Montes-Rodriguez, Banach spaces of hypercyclic vectors, Michi gan Math. J. 43. No. 3 (1996), 419-436.
    [12] P. S. Bourdon. Invariant manifolds of hypercyclic vectors. Proc. Amer. Math. Soc. 118, No. 3 (1993), 845-847.
    [13] S. Rolewicz, On orbits of elements, Studia Math. 32(1969), 17-22.
    [14] B. Beauzamy, Un operateur, sur l''espace de Hilbert, dont tour les polynomes sont hypercycliques, C. R. Acad. Sci. Paris Ser. I Math. 303(1986), 923-925.
    [15] D. A Herrero, Hypercyclic operators and chaos, J.Operator Theory 28(1992), 93-103.
    [16] G. D. Birkhoff. Demonstration d''un theoreme elementaire sur les fonctions entieres. C. R. Acad. Sci. Paris. 189(1929), 473-475.
    [17] T. Kato, Perturbation Theorem for Linear Operators, Spring-Verlag, New York, Berlin, 1966.
    [18] W. Desch, W. Schappacher, and G. Webb, Hypercyclic and chaotic semigroups of linear operators*, Ergod. Th. Dynam.Sys.(1997)17,793-819.
    [19] R. M. Gethner and J. H. Shapiro, Universal vectors for operators on spaces of holomorphic functions, Proc. Amer. Math. Soc. 100(2)(1987),281-288.
    igskip
    [20] C. Kitai, "Invariant Closed Sets for Linear Operators." Thesis, University Toronto,

    QR CODE
    :::