On operators satisfying T*{divides}T2{divides}T ≥ T*{divides}T{divides}2T

Abstract

Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce the class, denoted QA, of operators satisfying T*{divides}T2{divides}T ≥ T*{divides}T{divides}2T and we prove basic structural properties of these operators. Using these results, we also prove that if E is the Riesz idempotent for a non-zero isolated point λ{ring operator} of the spectrum of T ∈ QA, then E is self-adjoint, and we give a necessary and sufficient condition for T ⊗ S to be in QA when T and S are both non-zero operators. © 2006 Elsevier Inc. All rights reserved.