Linear operators for which T^∗T and T + T^∗ commute. III

Stephen LaVern Campbell

Vol. 76 (1978), No. 1, 17–19

DOI: 10.2140/pjm.1978.76.17

Abstract

Let Θ denote the set of all linear operators T acting on a separable Hilbert space ℋ for which T^∗T and T + T^∗ commute. It will be shown that if T ∈ Θ and T^∗ is hyponormal, then T is normal. Also if T ∈ Θ and T is hyponormal, then T is subnormal.

Mathematical Subject Classification 2000

Primary: 47B20

Milestones

Received: 21 March 1977

Published: 1 May 1978