Commutativity of selfadjoint operators

Mitsuru Uchiyama

Vol. 161 (1993), No. 2, 385–392

DOI: 10.2140/pjm.1993.161.385

Abstract

Nonnegative bounded operators A and B on a Hilbert space ℋ commute if ABⁿ + BⁿA ≥ 0 for n = 1,3,…, , or if e^tA ≤ e^tA+sB ≤ e^tA+s∥B∥ for every s,t > 0.

Mathematical Subject Classification 2000

Primary: 47B15

Secondary: 47A10

Milestones

Received: 20 November 1991

Revised: 20 October 1992

Published: 1 December 1993