Vol. 39, No. 3, 1971

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Convexity properties of a generalized numerical range

John Emanuel de Pillis

Vol. 39 (1971), No. 3, 767–781
Abstract

A numerical range Wn(A) of a bounded linear operator A on Hilbert space p is defined to be the set of complex numbers Wn(A) = {tr(AM) : dimension M = n} where M runs over all orthogonal n-dimensional projections on , and tr() is the trace functional. It is known that Wn(A) is always convex (the Hausdorff-Toeplitz theorem tells us that W1(A) is convex). In what follows, we replace the trace functional by the more general elementary symmetric functions, and derive certain convexity results.

Mathematical Subject Classification 2000
Primary: 47A10
Milestones
Received: 10 October 1969
Revised: 23 September 1970
Published: 1 December 1971
Authors
John Emanuel de Pillis