Vol. 67, No. 2, 1976

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On extreme points of the joint numerical range of commuting normal operators

Pushpa Juneja

Vol. 67 (1976), No. 2, 473–476

Let W(T) = {⟨Tx,x: x= 1;x H} denote the numerical range of a bounded normal operator T on a complex Hilbert space H. S. Hildebrandt has proved that if λ is an extreme point of W(T), the closure of W(T), and λ W(T) then λ is in the point spectrum of T. In this note, we shall prove an analogous result for an n-tuple of commuting bounded normal operators on H.

Mathematical Subject Classification 2000
Primary: 47A10
Received: 15 June 1976
Published: 1 December 1976
Pushpa Juneja