Eigenvalues in the boundary of the numerical range

Allan M. Sinclair

Vol. 35 (1970), No. 1, 231–234

DOI: 10.2140/pjm.1970.35.231

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