The study of operators satisfying σja（T ） = σa（T ） is of significant interest. Does σja（T ） = σa（T ） for n-perinormal operator T ∈ B（H）？ This question was raised by Mecheri and Braha [Oper. Matrices 6 ...The study of operators satisfying σja（T ） = σa（T ） is of significant interest. Does σja（T ） = σa（T ） for n-perinormal operator T ∈ B（H）？ This question was raised by Mecheri and Braha [Oper. Matrices 6 （2012）, 725-734]. In the note we construct a counterexample to this question and obtain the following result： if T is a n-perinormal operator in B（H）, then σja（T ）／{0} = σa（T ）／{0}. We also consider tensor product of n-perinormal operators.展开更多
This article has two purposes： the first is to give some structure results for the class of m-isometries, and the second purpose is to extend the notions of left and right inverses to m-left and m-right inverses resp...This article has two purposes： the first is to give some structure results for the class of m-isometries, and the second purpose is to extend the notions of left and right inverses to m-left and m-right inverses respectively.展开更多
The approximate point spectrum properties of p-ω-hyponormal operators are given and proved. In faet, it is a generalization of approximate point speetrum properties of ω- hyponormal operators. The relation of spectr...The approximate point spectrum properties of p-ω-hyponormal operators are given and proved. In faet, it is a generalization of approximate point speetrum properties of ω- hyponormal operators. The relation of spectra and numerical range of p-ω-hyponormal operators is obtained, On the other hand, for p-ω-hyponormal operators T,it is showed that if Y is normal,then T is also normal.展开更多
An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(...An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )■N(T~* ), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )■N(T ), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.展开更多
In this article, we study characterization, stability, and spectral mapping the- orem for Browder＇s essential spectrum, Browder＇s essential defect spectrum and Browder＇s essential approximate point spectrum of clos...In this article, we study characterization, stability, and spectral mapping the- orem for Browder＇s essential spectrum, Browder＇s essential defect spectrum and Browder＇s essential approximate point spectrum of closed densely defined linear operators on Banach spaces.展开更多
基金supported by NNSF(1122618511201126)the Basic Science and Technological Frontier Project of Henan Province(132300410261)
文摘The study of operators satisfying σja（T ） = σa（T ） is of significant interest. Does σja（T ） = σa（T ） for n-perinormal operator T ∈ B（H）？ This question was raised by Mecheri and Braha [Oper. Matrices 6 （2012）, 725-734]. In the note we construct a counterexample to this question and obtain the following result： if T is a n-perinormal operator in B（H）, then σja（T ）／{0} = σa（T ）／{0}. We also consider tensor product of n-perinormal operators.
文摘This article has two purposes： the first is to give some structure results for the class of m-isometries, and the second purpose is to extend the notions of left and right inverses to m-left and m-right inverses respectively.
文摘The approximate point spectrum properties of p-ω-hyponormal operators are given and proved. In faet, it is a generalization of approximate point speetrum properties of ω- hyponormal operators. The relation of spectra and numerical range of p-ω-hyponormal operators is obtained, On the other hand, for p-ω-hyponormal operators T,it is showed that if Y is normal,then T is also normal.
基金Supported by the Natural Science Foundation of the Department of Education of Henan Province（12B110025, 102300410012）
文摘An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )■N(T~* ), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )■N(T ), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.
文摘In this article, we study characterization, stability, and spectral mapping the- orem for Browder＇s essential spectrum, Browder＇s essential defect spectrum and Browder＇s essential approximate point spectrum of closed densely defined linear operators on Banach spaces.
