On properties of k -quasi-class A ( n ) operators

摘要

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.