Abstract
Let n and k be positive integers; an operator T ∈ B(H) is called a k-quasi-class A(n) operator if T ∗k (|T 1+n | 2 1+n - |T| 2 )T k ≥ 0, which is a common generalization of class A and class A(n) operators. In this paper, firstly we prove some basic structural properties of this class of operators, showing that if T is a k-quasi-class A(n) operator, then the nonzero points of its point spectrum and joint point spectrum are identical, the eigen-spaces corresponding to distinct eigenvalues of T are mutually orthogonal, the nonzero points of its approximate point spectrum and joint approximate point spectrum are identical; secondly we consider the tensor products for k-quasi-class A(n) operators, giving a necessary and sufficient condition for T ⊗ S to be a k-quasi-class A(n) operator when T and S are both nonzero operators. MSC: 47B20; 47A63
Highlights
Let H be a separable complex Hilbert space and C be the set of complex numbers
Firstly we prove some basic structural properties of this class of operators, showing that if T is a k-quasi-class A(n) operator, the nonzero points of its point spectrum and joint point spectrum are identical, the eigen-spaces corresponding to distinct eigenvalues of T are mutually orthogonal, the nonzero points of its approximate point spectrum and joint approximate point spectrum are identical; secondly we consider the tensor products for k-quasi-class
Which is called the absolute value of T and they showed that class A is a subclass of paranormal and contains p-hyponormal and log-hyponormal operators
Summary
Let H be a separable complex Hilbert space and C be the set of complex numbers. Let B(H) denote the C∗-algebra of all bounded linear operators acting on H. Which is called the absolute value of T and they showed that class A is a subclass of paranormal and contains p-hyponormal and log-hyponormal operators. For more interesting properties on class A(n) and n-paranormal operators, see [ – ]. T ∈ B(H) is called a k-quasi-class A(n) operator for positive integers n and k if. Let T ∈ B(H) be a k-quasi-class A(n) operator for positive integers n and k, and let T =. T ∈ B(H) is called a (n, k)-quasiparanormal operator for positive integers n and k if
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