Vol. 53, No. 2, 1974

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ISSN: 0030-8730
Linear operators for which TT and TT commute. II

Stephen LaVern Campbell

Vol. 53 (1974), No. 2, 355–361
Abstract

Let (BN) denote the class of all bounded linear operators on a Hilbert space such that τ τ and TT commute. Let (BN)+ be those τ (BN) which are hyponorma]. Embry has observed that if T (BN), then 0 W(T) or T is normal. This is used to show that if τ (BN), then (T + λI)(BN) unless T is normal. It is also shown that if τ (BN)+, then Tn is hyponormal for n 1. An example of a T (BN)+ such that T2(BN) is given. Paranormality of operators in (BN) is shown to be equivalent to hyponormality. The relationship between T being in (BN) and T being centered is discussed. Finally, all 3 ×3 matrices in (BN) are characterized.

Mathematical Subject Classification 2000
Primary: 47B20
Milestones
Received: 11 April 1973
Published: 1 August 1974
Authors
Stephen LaVern Campbell