位移算子的子空间亚超循环性
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摘要
利用超循环算子研究的方法,给出了一个判定亚超循环算子的充分条件,并且讨论了位移算子和加权位移算子的子空间亚超循环性性质.
With the methods of hypercyclic operator researches,a sufficient condition for a bounded linear operator to be supercyclic is obtained,and several properties of the subspace-supercyclic operators and are discussed.
With the methods of hypercyclic operator researches,a sufficient condition for a bounded linear operator to be supercyclic is obtained,and several properties of the subspace-supercyclic operators and are discussed.
引文
[1]BAYART F,MATHERON E.Dynamics of Linear Operators[M].Cambridge:Cambridge University Press,2009.
[2]KARL G.Grosse Erdmann,Afred Peris Manguillot,Linear Chaos[M].London:Springer-Verlag,2011.
[3]SHU Yong-lu,ZHAO Xian-feng.The Conjugate Class of a Supercyclic Operator[J].Complex Analysis and Operator Theory,2012,6(3):603-611.
[4]LEON-SAAVEDRA F,MULLER V.Rotations of Hypercyclic and Supercyclic Operators[J].Integral Equations and Operator Theory,2004,50(3):385-391.
[5]HERRERO D A.Limits of Hypercyclic and Supercyclic Operators[J].Journal of Functional Analysis,1991,99(1):179-190.
[6]KARAMI P,HABIBI M.On Density and Hypercyclicity[J].International Mathematical Forum,2013,8(9):401-405.
[7]BOURDON P S,FELDMAN N S.Somewhere Dense Orbits Are Everywhere Dense[J].Indiana Univ Math,2003,52(3):811-819.
[8]MADORE B F,MARTINEZ-AVENDANO R A.Subspace Hypercyclicity[J].Journal of Mathematical Analysis and Applications,2011,373(2):502-511.
[9]LE C M.On Subspace-Hypercyclic Operators[J].Amber Math Soc,2011,139(8):2847-2852.
[10]JIMENEZ-MUNGUIA R R,MARTINEZ-AVENDANO R A,PERIS A.Some Questions About Subspace Hypercyclic Operators[J].Journal of Mathematical Analysis and Applications,2013(4-8):209-212.
[11]REZAEI H.Notes on Subspace-Hypercyclic Operators[J].Journal of Mathematical Analysis and Applications,2013,397:428-433.
[12]ZHAO Xian-feng,SHU Yong-lu,ZHOU Yun-hua.Subspace-Supercyclicity and Common Subspace Supercyclic Vectors[J].华东师范大学学报:自然科学版,2012,2012(1):106-112.
[13]MONTES-RODRIGUEZ A,SALAS H N.Supercyclic Subspaces:Spectral Theory and Weighted Shifts[J].Advances in Mathematics,2001,163(1):74-134.
[14]赵显锋,舒永录.Supercyclic算子族的公共超循环向量[J].西南大学学报:自然科学版,2012,34(4):101-104.
[15]GROSSE-ERDMANN K G.Hypercyclic and Chaotic Weighted Shifts[J].Studia Math,2000,139(1):47-68.
[2]KARL G.Grosse Erdmann,Afred Peris Manguillot,Linear Chaos[M].London:Springer-Verlag,2011.
[3]SHU Yong-lu,ZHAO Xian-feng.The Conjugate Class of a Supercyclic Operator[J].Complex Analysis and Operator Theory,2012,6(3):603-611.
[4]LEON-SAAVEDRA F,MULLER V.Rotations of Hypercyclic and Supercyclic Operators[J].Integral Equations and Operator Theory,2004,50(3):385-391.
[5]HERRERO D A.Limits of Hypercyclic and Supercyclic Operators[J].Journal of Functional Analysis,1991,99(1):179-190.
[6]KARAMI P,HABIBI M.On Density and Hypercyclicity[J].International Mathematical Forum,2013,8(9):401-405.
[7]BOURDON P S,FELDMAN N S.Somewhere Dense Orbits Are Everywhere Dense[J].Indiana Univ Math,2003,52(3):811-819.
[8]MADORE B F,MARTINEZ-AVENDANO R A.Subspace Hypercyclicity[J].Journal of Mathematical Analysis and Applications,2011,373(2):502-511.
[9]LE C M.On Subspace-Hypercyclic Operators[J].Amber Math Soc,2011,139(8):2847-2852.
[10]JIMENEZ-MUNGUIA R R,MARTINEZ-AVENDANO R A,PERIS A.Some Questions About Subspace Hypercyclic Operators[J].Journal of Mathematical Analysis and Applications,2013(4-8):209-212.
[11]REZAEI H.Notes on Subspace-Hypercyclic Operators[J].Journal of Mathematical Analysis and Applications,2013,397:428-433.
[12]ZHAO Xian-feng,SHU Yong-lu,ZHOU Yun-hua.Subspace-Supercyclicity and Common Subspace Supercyclic Vectors[J].华东师范大学学报:自然科学版,2012,2012(1):106-112.
[13]MONTES-RODRIGUEZ A,SALAS H N.Supercyclic Subspaces:Spectral Theory and Weighted Shifts[J].Advances in Mathematics,2001,163(1):74-134.
[14]赵显锋,舒永录.Supercyclic算子族的公共超循环向量[J].西南大学学报:自然科学版,2012,34(4):101-104.
[15]GROSSE-ERDMANN K G.Hypercyclic and Chaotic Weighted Shifts[J].Studia Math,2000,139(1):47-68.