On joint numerical ranges

John J. Buoni and Bhushan L. Wadhwa

Vol. 77 (1978), No. 2, 303–306

DOI: 10.2140/pjm.1978.77.303

Abstract

The joint numerical status of commuting bounded operators A₁ and A₂ on a Hilbert space is defined as {(ϕ(A₁),ϕ(A₂)) such that ϕ is a state on the C∗-algebra generated by A₁ and A₂}. It is shown that if A₁ and A₂ are commuting normal operators then their joint numerical status equals the closure of their joint numerical range. It is also shown that certain points in the boundary of the joint numerical range are joint approximate reducing eigenvalues.

Mathematical Subject Classification 2000

Primary: 47A12

Milestones

Received: 7 October 1977

Published: 1 August 1978