Vol. 65, No. 2, 1976

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Commutators and numerical ranges of powers of operators

Elias Sai Wan Shiu

Vol. 65 (1976), No. 2, 517–523
Abstract

If 0 does not lie in the closure of the numerical range of any positive integral power of a Hilbert space operator T, then an odd power of T is normal. If, in addition, T is convexoid, then T itself is normal; in fact, T is the direct sum of at most three rotated positive operators. A version of these results is given in terms of commutators.

Mathematical Subject Classification 2000
Primary: 47B47
Secondary: 47A10
Milestones
Received: 24 November 1975
Revised: 30 March 1976
Published: 1 August 1976
Authors
Elias Sai Wan Shiu