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Global minimum and orthogonality in C1-classes

✍ Scribed by Salah Mecheri; Messaoud Bounkhel

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
187 KB
Volume
287
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper we characterize the global minimum of an arbitrary function defined on a Banach space, in terms of a new concept of derivatives adapted for our case from a recent work due to D.J. Keckic (J. Operator Theory, submitted for publication). Using these results we establish several new characterizations of the global minimum of the map F ψ : U β†’ R + defined by F ψ (X) = ψ(X) 1 , where ψ : U β†’ C 1 is a map defined by ψ(X) = S + Ο†(X) and Ο† : B(H ) β†’ B(H ) is a linear map, S ∈ C 1 , and U = {X ∈ B(H ): Ο†(X) ∈ C 1 }. Further, we apply these results to characterize the operators which are orthogonal to the range of elementary operators.

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