Vol. 35, No. 1, 1970

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Eigenvalues in the boundary of the numerical range

Allan M. Sinclair

Vol. 35 (1970), No. 1, 231–234
Abstract

We study eigenvalues λ of a continuous linear operator T on a complex Banach space X that lie in the boundary of the numerical range of T. We show that the kernel of T λI is orthogonal, in the sense of G. Birkhoff, to the range of T λI.

Mathematical Subject Classification
Primary: 47.30
Milestones
Received: 5 December 1969
Published: 1 October 1970
Authors
Allan M. Sinclair
The University of Edinburgh
The King’s Buildings
Edinburgh
EH9 3JZ
United Kingdom