<abstract xmlns="http://www.w3.org/1999/xhtml"> 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.</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.

The Gâteaux derivative and orthogonality in C∞

Department of Mathematics, Taibah University, College of Science, Department of Mathematics, P.O.Box 30002, Al Madinah Almunawwarah, Saudi Arabia

Department of Mathematics, Tebessa University, College of Science, Department of Mathematics, 12002 Tebessa, Algeria (Algérie).

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

The Gâteaux derivative and orthogonality in C

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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...

The Gâteaux derivative and orthogonality in C_∞

Published Online: May 17, 2013

Page range: 275 - 284

DOI: https://doi.org/10.2478/v10309-012-0018-3

Keywords
Elementary, operators, Compact operators, orthogonality, Gateaux derivative

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