| Titre : | Summability properties and the positive operators | | Titre original : | Propriétés de sommabilité et les opérateurs positifs | | Type de document : | texte manuscrit | | Auteurs : | Halima Hamdi, Auteur ; Amar Belacel, Directeur de thèse | | Editeur : | Laghouat : Université Amar Telidji - Département de mathématiques | | Année de publication : | 2022 | | Importance : | 69 p | | Format : | 27 cm | | Accompagnement : | 1 disque optique numérique (CD-ROM) | | Note générale : | Option : Analyse mathématique | | Langues : | Anglais | | Catégories : | THESES :05 mathématique
| | Mots-clés : | Homogeneous polynomials Banach lattice Positive p-summing operators Positive strongly p−summing operators Tensor norm multiple Cohen strongly summing operators Pietsch domination theorem Positive strongly p-summing multilinear operators | | Résumé : | The purpose of this thesis is to develop some notions and theorems of positive p-summability for multilinear operators and homogeneous polynomials. Throughout this work, first. We extend the notion of strongly p-summing multilinear operators by Dimant, in (J. Math. Anal. Appl. 278, 182 − 193(2003)), to the positive framework, and prove among other results, the domination, inclusion and composition theorems. As consequence, we investigate some connections between our class and other classes of operators through, duality and linearization. Then, we compare our new class of multiple Cohen positive strongly p-summing multilinear operators along with different classes of positive multilinear p-summability and investigate a duality relationship in terms of tensor norm. Finally, we introduce the concepts of Cohen positive strongly p-summing and positive p-dominated m-homogeneous polynomials. We prove a version of Pietsch’s domination theorem for the first class among other results, and a Butype theorem, as well as some inclusions with other known spaces. Moreover, we present a characterization of these classes in tensor terms. | | note de thèses : | Thèse de doctorat en mathématiques |
Summability properties and the positive operators = Propriétés de sommabilité et les opérateurs positifs [texte manuscrit] / Halima Hamdi, Auteur ; Amar Belacel, Directeur de thèse . - Laghouat : Université Amar Telidji - Département de mathématiques, 2022 . - 69 p ; 27 cm + 1 disque optique numérique (CD-ROM). Option : Analyse mathématique Langues : Anglais | Catégories : | THESES :05 mathématique
| | Mots-clés : | Homogeneous polynomials Banach lattice Positive p-summing operators Positive strongly p−summing operators Tensor norm multiple Cohen strongly summing operators Pietsch domination theorem Positive strongly p-summing multilinear operators | | Résumé : | The purpose of this thesis is to develop some notions and theorems of positive p-summability for multilinear operators and homogeneous polynomials. Throughout this work, first. We extend the notion of strongly p-summing multilinear operators by Dimant, in (J. Math. Anal. Appl. 278, 182 − 193(2003)), to the positive framework, and prove among other results, the domination, inclusion and composition theorems. As consequence, we investigate some connections between our class and other classes of operators through, duality and linearization. Then, we compare our new class of multiple Cohen positive strongly p-summing multilinear operators along with different classes of positive multilinear p-summability and investigate a duality relationship in terms of tensor norm. Finally, we introduce the concepts of Cohen positive strongly p-summing and positive p-dominated m-homogeneous polynomials. We prove a version of Pietsch’s domination theorem for the first class among other results, and a Butype theorem, as well as some inclusions with other known spaces. Moreover, we present a characterization of these classes in tensor terms. | | note de thèses : | Thèse de doctorat en mathématiques |
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Summability properties and the positive operators
