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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 603041, 6 pages
doi:10.1155/2009/603041

A Note on the Range of the Operator X↦TX−XT Defined on 𝒞2(ℋ)

Vasile Lauric

Department of Mathematics, Florida A\&M University, Tallahassee, FL 32307, USA

Abstract

We show how a proof of J. Stampfli can be extended to prove that the operator X↦TX−XT defined on the Hilbert-Schmidt class, when T is an M-hyponormal, p-hyponormal, or log-hyponormal operator, has a closed range if and only if σ(T) is finite.