Let H be a complex Hilbert space with dimH ≥3, Bs（H） the （real） Jordan algebra of all self-adjoint operators on H. Every surjective map Ф ： Bs（H）→13s（H） preserving numerical radius of operator products （r...Let H be a complex Hilbert space with dimH ≥3, Bs（H） the （real） Jordan algebra of all self-adjoint operators on H. Every surjective map Ф ： Bs（H）→13s（H） preserving numerical radius of operator products （respectively, Jordan triple products） is characterized. A characterization of surjective maps on Bs （H） preserving a cross operator norm of operator products （resp. Jordan triple products of operators） is also given.展开更多
Quantum uncertainty relations are mathematical inequalities that describe the lower bound of products of standard deviations of observables(i.e.,bounded or unbounded self-adjoint operators).By revealing a connection b...Quantum uncertainty relations are mathematical inequalities that describe the lower bound of products of standard deviations of observables(i.e.,bounded or unbounded self-adjoint operators).By revealing a connection between standard deviations of quantum observables and numerical radius of operators,we establish a universal uncertainty relation for k observables,of which the formulation depends on the even or odd quality of k.This universal uncertainty relation is tight at least for the cases k=2 and k=3.For two observables,the uncertainty relation is a simpler reformulation of Schr?dinger’s uncertainty principle,which is also tighter than Heisenberg’s and Robertson’s uncertainty relations.展开更多
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
It is shown that for any two n x n complex valued matrices A, B the inequality ｜perA-perB｜≤n｜｜A-B｜｜Fmax（｜｜A｜｜F,｜｜B｜｜F）^n-1 or ｜perA-perB｜≤｜｜A｜｜F^n＋｜｜B｜｜F^n holds for ｜｜A｜｜F =（∑i=1^n...It is shown that for any two n x n complex valued matrices A, B the inequality ｜perA-perB｜≤n｜｜A-B｜｜Fmax（｜｜A｜｜F,｜｜B｜｜F）^n-1 or ｜perA-perB｜≤｜｜A｜｜F^n＋｜｜B｜｜F^n holds for ｜｜A｜｜F =（∑i=1^n∑j=1^n｜αij｜^2）^1/2 where A^H denotes the conjuagte transpose of the matrix A = （αij）n×n.展开更多
In this article, we give an operator transform T （＊） from class A operator to the class of hyponormal operators. It is different from the operator transform T defined by M. Ch and T. Yamazaki. Then, we show that σ...In this article, we give an operator transform T （＊） from class A operator to the class of hyponormal operators. It is different from the operator transform T defined by M. Ch and T. Yamazaki. Then, we show that σ（T ） = σ（ T （＊）） and σa（T ）／{0} = σa（ T （＊））／{0}, in case T belongs to class A. Next, we obtain some relations between T and T （9）.展开更多
In this article,we refine certain earlier existing bounds for Berezin number of operator matrices.We also prove some new Berezin number inequalities for general n×n operator matrices.Further,we establish several ...In this article,we refine certain earlier existing bounds for Berezin number of operator matrices.We also prove some new Berezin number inequalities for general n×n operator matrices.Further,we establish several upper bounds for Berezin number and generalized Euclidean Berezin number for off-diagonal operator matrices.Finally,some interesting examples are discussed.展开更多
The electron and heavy hole energy levels of two vertically coupled In As hemispherical quantum dots/wetting layers embedded in a Ga As barrier are calculated numerically. As the radius increases, the electronic energ...The electron and heavy hole energy levels of two vertically coupled In As hemispherical quantum dots/wetting layers embedded in a Ga As barrier are calculated numerically. As the radius increases, the electronic energies increase for the small base radii and decrease for the larger ones. The energies decrease as the dot height increases. The intersubband and interband transitions of the system are also studied. For both, a spectral peak position shift to lower energies is seen due to the vertical coupling of dots. The interband transition energy decreases as the dot size increases, decreases for the dot shapes with larger heights, and reaches a minimum for coupled semisphere dots.展开更多
基金Supported by National Science Foundation of China (Grant Nos. 10771157, 10871111)the Provincial Science Foundation of Shanxi (Grant No. 2007011016)the Research Fund of Shanxi for Returned Scholars (Grant No. 2007-38)
文摘Let H be a complex Hilbert space with dimH ≥3, Bs（H） the （real） Jordan algebra of all self-adjoint operators on H. Every surjective map Ф ： Bs（H）→13s（H） preserving numerical radius of operator products （respectively, Jordan triple products） is characterized. A characterization of surjective maps on Bs （H） preserving a cross operator norm of operator products （resp. Jordan triple products of operators） is also given.
基金Supported by National Natural Science Foundation of China(Grant Nos.11771011,12071336)。
文摘Quantum uncertainty relations are mathematical inequalities that describe the lower bound of products of standard deviations of observables(i.e.,bounded or unbounded self-adjoint operators).By revealing a connection between standard deviations of quantum observables and numerical radius of operators,we establish a universal uncertainty relation for k observables,of which the formulation depends on the even or odd quality of k.This universal uncertainty relation is tight at least for the cases k=2 and k=3.For two observables,the uncertainty relation is a simpler reformulation of Schr?dinger’s uncertainty principle,which is also tighter than Heisenberg’s and Robertson’s uncertainty relations.
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It is shown that for any two n x n complex valued matrices A, B the inequality ｜perA-perB｜≤n｜｜A-B｜｜Fmax（｜｜A｜｜F,｜｜B｜｜F）^n-1 or ｜perA-perB｜≤｜｜A｜｜F^n＋｜｜B｜｜F^n holds for ｜｜A｜｜F =（∑i=1^n∑j=1^n｜αij｜^2）^1/2 where A^H denotes the conjuagte transpose of the matrix A = （αij）n×n.
基金supported by Science Foundation of Ministry of Education of China (208081)Technology and pioneering project in Henan Provice (102300410012)Education Foundation of Henan Province (2007110016, 2008B110006)
文摘In this article, we give an operator transform T （＊） from class A operator to the class of hyponormal operators. It is different from the operator transform T defined by M. Ch and T. Yamazaki. Then, we show that σ（T ） = σ（ T （＊）） and σa（T ）／{0} = σa（ T （＊））／{0}, in case T belongs to class A. Next, we obtain some relations between T and T （9）.
文摘In this article,we refine certain earlier existing bounds for Berezin number of operator matrices.We also prove some new Berezin number inequalities for general n×n operator matrices.Further,we establish several upper bounds for Berezin number and generalized Euclidean Berezin number for off-diagonal operator matrices.Finally,some interesting examples are discussed.
文摘The electron and heavy hole energy levels of two vertically coupled In As hemispherical quantum dots/wetting layers embedded in a Ga As barrier are calculated numerically. As the radius increases, the electronic energies increase for the small base radii and decrease for the larger ones. The energies decrease as the dot height increases. The intersubband and interband transitions of the system are also studied. For both, a spectral peak position shift to lower energies is seen due to the vertical coupling of dots. The interband transition energy decreases as the dot size increases, decreases for the dot shapes with larger heights, and reaches a minimum for coupled semisphere dots.
