The norm of a certain derivation

Charles Alan McCarthy

Vol. 53 (1974), No. 2, 515–518

DOI: 10.2140/pjm.1974.53.515

Abstract

J. C. Stampfli has asked whether the norm of the derivation Q_T : A → TA − AT as a mapping of the subalgebra A of B(H) into B(H) is given by inf{2∥T − A′∥ : A′∈ A′}. That this need not be the case is shown through an example in 4 × 4 matrices.

Mathematical Subject Classification 2000

Primary: 46L05

Secondary: 47B47

Milestones

Received: 2 May 1973

Published: 1 August 1974