In this paper we characterize the left joint spectrum of an n-tuple T = (T1,… ,Tn) of dominant bounded linear operators on a complex Hilbert space H and the unital C-algebra C(T) generated by T1, …,Tn and Ⅰ; moreov...In this paper we characterize the left joint spectrum of an n-tuple T = (T1,… ,Tn) of dominant bounded linear operators on a complex Hilbert space H and the unital C-algebra C(T) generated by T1, …,Tn and Ⅰ; moreover, we give an application of this characterization.展开更多
The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-def...The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-definite operators, the following conclusions are obtained: if a fourth order differential operator with a self-adjoint boundary condition that is left-definite and right-indefinite, then all its eigenvalues are real, and there exist countably infinitely many positive and negative eigenvalues which are unbounded from below and above, have no finite cluster point and can be indexed to satisfy the inequality …≤λ-2≤λ-1≤λ-0〈0〈λ0≤λ1≤λ2≤…展开更多
文摘In this paper we characterize the left joint spectrum of an n-tuple T = (T1,… ,Tn) of dominant bounded linear operators on a complex Hilbert space H and the unital C-algebra C(T) generated by T1, …,Tn and Ⅰ; moreover, we give an application of this characterization.
基金Supported by the National Natural Science Foundation of China(10561005)the Doctor's Discipline Fund of the Ministry of Education of China(20040126008)
文摘The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-definite operators, the following conclusions are obtained: if a fourth order differential operator with a self-adjoint boundary condition that is left-definite and right-indefinite, then all its eigenvalues are real, and there exist countably infinitely many positive and negative eigenvalues which are unbounded from below and above, have no finite cluster point and can be indexed to satisfy the inequality …≤λ-2≤λ-1≤λ-0〈0〈λ0≤λ1≤λ2≤…