Given an n×n complex matrix A and an n-dimensional complex vector y=(ν1 , ··· , νn ), the y-numerical radius of A is the nonnegative quantity ry(A)=max{n∑j=1ν*jAx︱:Axj︱: x*jxj=1,xj ∈Cn}.Here...Given an n×n complex matrix A and an n-dimensional complex vector y=(ν1 , ··· , νn ), the y-numerical radius of A is the nonnegative quantity ry(A)=max{n∑j=1ν*jAx︱:Axj︱: x*jxj=1,xj ∈Cn}.Here Cn is an n-dimensional linear space overthe complex field C. For y = (1, 0, ··· , 0) it reduces to the classical radius r(A) =max {|x*Ax|: x*x=1}.We show that ry is a generalized matrix norm if and only ifn∑j=1νj≠ 0.Next, we study some properties of the y-numerical radius of matrices andvectors with non-negative entries.展开更多
Let A be an n×n complex matrix,and let y =(α1,...,αn) be an n-dimensional complex vector.The y-numerical radius of A,denoted by ry(A),is defined follows:r_y(A) = max {|sum form i=1 to n α_ix_i~* Ax_i|:x_i~* x_...Let A be an n×n complex matrix,and let y =(α1,...,αn) be an n-dimensional complex vector.The y-numerical radius of A,denoted by ry(A),is defined follows:r_y(A) = max {|sum form i=1 to n α_ix_i~* Ax_i|:x_i~* x_i = 1,x_i ∈ C^n},where Cn is an n-dimensional vector space over complex field C.In this paper we studynorm properties and stability of y-numerical radius.展开更多
Let f be a homeomorphism of a compact tvs-cone metric space. In this paper,we show that f is tvs-cone expansive if and only if f has a generator. Further, it is proved that if f is tvs-cone expansive, then the set of ...Let f be a homeomorphism of a compact tvs-cone metric space. In this paper,we show that f is tvs-cone expansive if and only if f has a generator. Further, it is proved that if f is tvs-cone expansive, then the set of points having converging semiorbits under f is a countable set. Results of this paper improve some expansive homeomorphisms theorems in topological dynamics, which will help to research dynamical properties for homeomorphisms of tvs-cone metric spaces.展开更多
基金Foundation item： Supported by the Natural Science Foundation of Hubei Province（B20114410）
文摘Given an n×n complex matrix A and an n-dimensional complex vector y=(ν1 , ··· , νn ), the y-numerical radius of A is the nonnegative quantity ry(A)=max{n∑j=1ν*jAx︱:Axj︱: x*jxj=1,xj ∈Cn}.Here Cn is an n-dimensional linear space overthe complex field C. For y = (1, 0, ··· , 0) it reduces to the classical radius r(A) =max {|x*Ax|: x*x=1}.We show that ry is a generalized matrix norm if and only ifn∑j=1νj≠ 0.Next, we study some properties of the y-numerical radius of matrices andvectors with non-negative entries.
基金Supported by the Natural Science Foundation of Hubei Province（2004X157）
文摘Let A be an n×n complex matrix,and let y =(α1,...,αn) be an n-dimensional complex vector.The y-numerical radius of A,denoted by ry(A),is defined follows:r_y(A) = max {|sum form i=1 to n α_ix_i~* Ax_i|:x_i~* x_i = 1,x_i ∈ C^n},where Cn is an n-dimensional vector space over complex field C.In this paper we studynorm properties and stability of y-numerical radius.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1130136761472469+1 种基金11461005)the Doctoral Fund of Ministry of Education of China(Grant No.20123201120001)
文摘Let f be a homeomorphism of a compact tvs-cone metric space. In this paper,we show that f is tvs-cone expansive if and only if f has a generator. Further, it is proved that if f is tvs-cone expansive, then the set of points having converging semiorbits under f is a countable set. Results of this paper improve some expansive homeomorphisms theorems in topological dynamics, which will help to research dynamical properties for homeomorphisms of tvs-cone metric spaces.
