Vol. 33, No. 3, 1970

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The norm of a derivation

Joseph Gail Stampfli

Vol. 33 (1970), No. 3, 737–747
Abstract

In this paper, we determine the norm of the inner derivation QT : A TAAT acting on the Banach algebra B(H) of all bounded linear operators on Hilbert space. More precisely, we show that QT= inf{2T λI: λ complex }. If T is normal, then QTcan be specified in terms of the geometry of the spectrum of T.

Mathematical Subject Classification
Primary: 46.65
Milestones
Received: 2 September 1969
Revised: 15 December 1969
Published: 1 June 1970
Authors
Joseph Gail Stampfli