Vol. 77, No. 2, 1978

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On joint numerical ranges

John J. Buoni and Bhushan L. Wadhwa

Vol. 77 (1978), No. 2, 303–306

The joint numerical status of commuting bounded operators A1 and A2 on a Hilbert space is defined as {(ϕ(A1)(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
Received: 7 October 1977
Published: 1 August 1978
John J. Buoni
Bhushan L. Wadhwa