Ky-Fan norm and its applications in inequalities between spectral values
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Date
2022
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Abstract
Our main goal in this thesis, is to improve or find some important inequalities related
to the usual operator norm and the numerical radius by using the Ky−F an norm defined
on K(H) space of compact linear operators on the complex Hilbert space, we study the
most important properties of this norm, trying to get satisfactory results.Notre objectif principal dans cette m ́emoire, est d’am ́eliorer ou de trouver certaines
in ́egalit ́es importantes li ́ees `a la norme de l’op ́erateur usuel et au rayon num ́erique en
utilisant la norme Ky −F an. d ́efinie sur l’espace K(H) des op ́erateurs lin ́eaires compacts
sur l’espace de Hilbert complexe, nous ́etudier les propri ́et ́es les plus importantes de cette
norme, en essayant d’obtenir des r ́esultats satisfaisants.Our main goal in this thesis, is to improve or find some important inequalities related
to the usual operator norm and the numerical radius by using the Ky−F an norm defined
on K(H) space of compact linear operators on the complex Hilbert space, we study the
most important properties of this norm, trying to get satisfactory results.
Description
mémoire master mathématique
Keywords
Complex Hilbert space, bounded linear operators, compact operators, spec- trum, numerical range, usual operator norm, spectral radius, numerical radius., Espace de Hilbert complexe, op ́erateurs lin ́eaires born ́es, op ́erateurs com- pacts, spectre, domaine num ́erique, norme usuelle des op ́erateurs, rayon spectral, rayon num ́erique, norme de Ky − F an.
Citation
universite of el oued