On the Supercyclicity and Hypercyclicity of the Operator Algebra  

作　　者：B.YOUSEFI H.REZAEI 

机构地区：[1]Department of Mathematics,College of Sciences,Shiraz University,Shiraz 71454,Iran and Department of Mathematics,Payame-Noor University,Iran

出　　处：《Acta Mathematica Sinica,English Series》2008年第7期1221-1232,共12页数学学报（英文版）

摘　　要：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.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.

关 键 词：operator algebra ＊-strong topology strong operator topology hypercyclicity criterion supercyclicity criterion 

分 类 号：O153[理学—数学]