Vol. 72, No. 2, 1977

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Wδ(T) is convex

J. Kyle

Vol. 72 (1977), No. 2, 483–485
Abstract

Stampfli introduced a generalization of the numerical range for any bounded linear operator T on a Hilbert space . This is denoted by Wδ(T) and is defined by

Wδ(T) = closure {⟨T x,x⟩ : ∥x ∥ = 1 and ∥T x∥ ≧ δ}.

Stampfli asked whether Wδ(T) is convex. In this short note we provide an affirmative answer to this question.

Mathematical Subject Classification 2000
Primary: 47A10
Milestones
Received: 15 February 1977
Published: 1 October 1977
Authors
J. Kyle