TENSOR PRODUCTS AND THE SPECTRAL CONTINUITY FOR κ-QUASI-*-CLASS A OPERATORS

An operator T 2 B(H) is called k-quasi- -class A if T k (|T 2 | |T | 2 )T k 0 for a positive integer k, which is a common generalization of -class A and quasi- -class A. In this paper, firstly we prove some inequalities of this class of operators; secondly we consider the tensor products for k-quasi- -class A operators, giving a necessary and sucient condition for