Let B（X） be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or ＊-strong topology. We give sufficient conditions for a continuous linear mapping L...Let B（X） be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or ＊-strong topology. We give sufficient conditions for a continuous linear mapping L ： B（X） →B（X） to be supercyclic or ,-supercyclic. In particular our condition implies the existence of an infinite dimensional subspace of supercyclic vectors for a mapping T on H. Hypercyclicity of the operator algebra with strong operator topology was studied＇ by Chan and here we obtain an analogous result in the case of ＊-strong operator topology.展开更多
Let X be a separable infinite dimensional Banach space and B（X） denote its operator algebra, the algebra of all bounded linear operators T ： X → X. Define a left multiplication mapping LT ： B（X）→B（X） by LT（...Let X be a separable infinite dimensional Banach space and B（X） denote its operator algebra, the algebra of all bounded linear operators T ： X → X. Define a left multiplication mapping LT ： B（X）→B（X） by LT（V） → TV, V ∈ B（X）. We investigate the connections between hypercyclic and chaotic behaviors of the left multiplication mapping LT on S（Z） and that of operator T on X. We obtain that LT is SOT-hypercyclic if and only if T satisfies the Hypercyclicity Criterion. If we define chaos on B（X） as SOT-hypercyclicity plus SOT-dense subset of periodic points, we also get that LT is chaotic if and only if T is chaotic in the sense of Devaney.展开更多
文摘Let B（X） be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or ＊-strong topology. We give sufficient conditions for a continuous linear mapping L ： B（X） →B（X） to be supercyclic or ,-supercyclic. In particular our condition implies the existence of an infinite dimensional subspace of supercyclic vectors for a mapping T on H. Hypercyclicity of the operator algebra with strong operator topology was studied＇ by Chan and here we obtain an analogous result in the case of ＊-strong operator topology.
基金Supported by the Science Foundation of Department of Education of Anhui Province (Grant No. KJ2008B249)the Foundation of Hefei University (Grant No. RC039)
文摘Let X be a separable infinite dimensional Banach space and B（X） denote its operator algebra, the algebra of all bounded linear operators T ： X → X. Define a left multiplication mapping LT ： B（X）→B（X） by LT（V） → TV, V ∈ B（X）. We investigate the connections between hypercyclic and chaotic behaviors of the left multiplication mapping LT on S（Z） and that of operator T on X. We obtain that LT is SOT-hypercyclic if and only if T satisfies the Hypercyclicity Criterion. If we define chaos on B（X） as SOT-hypercyclicity plus SOT-dense subset of periodic points, we also get that LT is chaotic if and only if T is chaotic in the sense of Devaney.
