The closure of the numerical range contains the spectrum

Eduardo H. Zarantonello

Vol. 22 (1967), No. 3, 575–595

DOI: 10.2140/pjm.1967.22.575

Abstract

The purpose of this paper is to show that the well known theorem in the theory of linear operators in Hilbert space indicated in the title holds for nonlinear operators and to a certain extent for noncontinuous ones, and to provide a constructive method for solving the equations involved.

Mathematical Subject Classification

Primary: 47.30

Milestones

Received: 20 January 1965

Published: 1 September 1967