On k-Quasiclass A Operators

Abstract

An operator T∈B(ℋ) is called k-quasiclass A if T∗k(|T2|−|T|2)Tk≥0 for a positive integer k, which is a common generalization of quasiclass A. In this paper, firstly we prove some inequalities of this class of operators; secondly we prove that if T is a k-quasiclass A operator, then T is isoloid and T−λ has finite ascent for all complex number λ; at last we consider the tensor product for k-quasiclass A operators.