The Gâteaux derivative and orthogonality in C∞

Salah Mecheri; Hacene Mecheri

doi:10.2478/v10309-012-0018-3

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The Gâteaux derivative and orthogonality in C∞

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 20 (2012): Issue 1 (May 2012)

By: Salah Mecheri and Hacene Mecheri

Open Access

|May 2013

Abstract

The general problem in this paper is minimizing the C_∞− norm of suitable affine mappings from B(H) to C_∞, using convex and differential analysis (Gateaux derivative) as well as input from operator theory. The mappings considered generalize the so-called elementary operators and in particular the generalized derivations, which are of great interest by themselves. The main results obtained characterize global minima in terms of (Banach space) orthogonality.

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