Gâteaux Derivative and Orthogonality INC1-CLASSES (original) (raw)
The general problem in this paper is minimizing the C1(H)-norm of suitable affine mappings from B(H) to C1(H), using convex and differential analysis (Gâteaux 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
Related papers
Gâteaux derivative and orthogonality in -classes
Journal of Inequalities in Pure & Applied Mathematics, 2006
The general problem in this paper is minimizing the Cp norm of suitable affine mappings from B(H) to Cp, 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, and constitute an interesting combination of infinite-dimensional differential analysis, operator theory and duality. Note that the results obtained generalize all results in the literature concerning operator which are orthogonal to the range of a derivation and the techniques used have not been done by other authors.
of Inequalities in Pure and Applied Mathematics GÂTEAUX DERIVATIVE AND ORTHOGONALITY IN C 1-CLASSES
2005
The general problem in this paper is minimizing the Cp− norm of suitable affine mappings fromB(H) to Cp, 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, and constitute an interesting combination of infinite-dimensional differential analysis, operator theory and duality. Note that the results obtained generalize all results in the literature concerning operator which are orthogonal to the range of a derivation and the techniques used have not been done by other authors.
The Gâteaux derivative and orthogonality in C∞
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2012
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.
GÂTEAUX DERIVATIVE AND ORTHOGONALITY IN Cp-CLASSES
2013
ABSTRACT. The general problem in this paper is minimizing the Cp − norm of suitable affine mappings from B(H) to Cp, 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, and constitute an interesting combination of infinite-dimensional differential analysis, operator theory and duality. Note that the results obtained generalize all results in the literature concerning operator which are orthogonal to the range of a derivation and the techniques used have not been done by other authors.
A study of optimization in Hilbert Space
1998
The primary objective ofthis project is to demonstrate that a certain field ofoptimization can be effectively unified by afew geometric principles ofcomplete normed linear space theory.By employing these principles,important and complex finite dimensional problems can be interpreted and solved by methods springingfrom geometric insight. Concepts such as distance, orthogonality, and convexity play afundamental and indispensable role in this development. Viewed in these terms,seemingly diverse problems and techniques often arefound to be closely related.
Minimization of Quadratic Functionals Through Γ-Hilbert Space
2022
In this article we introduce the Gateaux differential and Frechet differential in Γ-Hilbert space. We show the examples and related theorems in this space. We have noticed that two differentials mentioned above will be equal for certain condition. Also, we discuss the relative extremum and the stationary point of a functional in Γ-Hilbert space. We already investigated the characteristics of both bounded and unbounded operators of Γ-Hilbert space. Now, by using previous concept we elaborate optimization problems and extremum of quadratic functionals in Γ-Hilbert space. Here we observe that how the function of the solution of a operator equation minimizes the quadratic functionals. Finally we describe the Minimization of quadratic functionals and its related theorem via Γ-Hilbert space.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.