In this paper,we observe a special kind of continuous functions on graphs.By estimating the integrals of these functions,we prove that there are no sensitive commutative group actions on graphs.Furthermore,we consider...In this paper,we observe a special kind of continuous functions on graphs.By estimating the integrals of these functions,we prove that there are no sensitive commutative group actions on graphs.Furthermore,we consider a 1-dimensional continuum composed of a spiral curve and a circle and show that there exist sensitive homeomorphisms on it,which answers negatively a question proposed by Kato in 1993.展开更多
In this paper,a generalized Toeplitz operator is defined and some of results about the classical Toeplitz operator are generalized.In particular,we obtain the necessary and sufficient condition for the product of two ...In this paper,a generalized Toeplitz operator is defined and some of results about the classical Toeplitz operator are generalized.In particular,we obtain the necessary and sufficient condition for the product of two such Toeplitz operators to still be Toeplitz operator and the necessary and sufficient condition for such Toeplitz operator to be normal operator.Finally,a necessary condition for two such Toeplitz operators to be commutative is established.展开更多
基金the Special Foundation of National Prior Basic Researches of China(Grant No.G1999075108)partially supported by the National Natural Science Foundation of China(Grant No.10501042)
文摘In this paper,we observe a special kind of continuous functions on graphs.By estimating the integrals of these functions,we prove that there are no sensitive commutative group actions on graphs.Furthermore,we consider a 1-dimensional continuum composed of a spiral curve and a circle and show that there exist sensitive homeomorphisms on it,which answers negatively a question proposed by Kato in 1993.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10801103, 10801126 and 10871142)Natural Sciences Fund for Colleges and Universities in Jiangsu Province (Grant No. 08KJB110010)
文摘In this paper, using the integral method observed by Mai Jiehua recently, we show that no dendrite admits a sensitive commutative group action.
基金Foundation item： the Natural Science Foundation of Jiangxi Province （No. 2007GZS0371）
文摘In this paper,a generalized Toeplitz operator is defined and some of results about the classical Toeplitz operator are generalized.In particular,we obtain the necessary and sufficient condition for the product of two such Toeplitz operators to still be Toeplitz operator and the necessary and sufficient condition for such Toeplitz operator to be normal operator.Finally,a necessary condition for two such Toeplitz operators to be commutative is established.
