Dahmane Achour | University Of Msila (original) (raw)
Papers by Dahmane Achour
In this paper, we obtain a new characterization of Hilbert spaces by means of polynomial mappings... more In this paper, we obtain a new characterization of Hilbert spaces by means of polynomial mappings, extending the linear result of Kwapie´n.
La notion des opérateurs p−lattice sommants aété introduite etétudiée par Yannovskii dans [10] po... more La notion des opérateurs p−lattice sommants aété introduite etétudiée par Yannovskii dans [10] pour p = 1 et généralisée par Nielsen et Szulga dans [7] et [8]. Dans ce papier, onétudie les opérateurs sous-linéaires p−lattice sommants. On essaie de caractériser ces opérateurs comme dans le cas linéaire. On conjecture que certaines propriétés (qui sont liées les unes aux autres) valables dans le cas linéaire seront aussi valables dans le cas sous linéaire. Si l'une des conjectures est vraie, on pourra montrer que le théorème de Grothendieck pour le cas sous linéaire ne sera pas valide. 2000 Mathematics Subject Classification. 46B42, 46B40, 47B460, 47B65.
Rendiconti del Circolo Matematico di Palermo, 2011
In this paper we introduce and study a new class containing the class of absolutely summing multi... more In this paper we introduce and study a new class containing the class of absolutely summing multilinear mappings, which we call absolutely (p;q 1,…,q m ;r)-summing multilinear mappings. We investigate some interesting properties concerning the absolutely (p;q 1,…,q m ;r)-summing m-linear mappings defined on Banach spaces. In particular, we prove a kind of Pietsch’s Domination Theorem and a multilinear version of the Factorization Theorem.
Annals of Functional Analysis, 2011
In this paper we consider the ideal of Cohen p-nuclear multilinear mappings, which is a natural m... more In this paper we consider the ideal of Cohen p-nuclear multilinear mappings, which is a natural multilinear extension of the ideal of p-nuclear linear operators. The space of Cohen p-nuclear m-linear mappings is characterized by means of a suitable tensor norm up to an isometric isomorphism.
Further Progress in Analysis - Proceedings of the 6th International ISAAC Congress, 2009
Colloquium Mathematicum, 2010
Linear and Multilinear Algebra, 2013
ABSTRACT We introduce the new ideal of strongly[Inline formula]-continuous linear operators in or... more ABSTRACT We introduce the new ideal of strongly[Inline formula]-continuous linear operators in order to study the adjoints of the [Inline formula]-absolutely continuous linear operators. Starting from this ideal we build a new multi-ideal by using the composition method. We prove the corresponding Pietsch domination theorem and we present a representation of this multi-ideal by a tensor norm. A factorization theorem characterizing the corresponding multi-ideal – which is also new for the linear case – is given. When applied to the case of the Cohen strongly [Inline formula]-summing operators, this result gives also a new factorization theorem.
Journal of Mathematical Analysis and Applications, 2007
In this paper, we introduce and study a new concept of summability in the category of multilinear... more In this paper, we introduce and study a new concept of summability in the category of multilinear operators, which is the Cohen strongly p-summing multilinear operators. We prove a natural analog of the Pietsch domination theorem and we compare the notion of p-dominated multilinear operators with this class by generalizing a theorem of Bu-Cohen.
Journal of Mathematical Analysis and Applications, 2013
ABSTRACT In this paper, we obtain a new characterization of Hilbert spaces by means of polynomial... more ABSTRACT In this paper, we obtain a new characterization of Hilbert spaces by means of polynomial mappings, extending the linear result of Kwapień. Keywords46G25-47H60 MSC2000Homogeneous polynomials-Cohen stronglyp-summing-absolutelyp-summing- p-dominated-stronglyp-summing-Pietsch domination theorem
atlas-conferences.com
... Beti Andonovic Coherent Proximate Nets and Strong Shape of Metric Compacta Risto Atanasov Geo... more ... Beti Andonovic Coherent Proximate Nets and Strong Shape of Metric Compacta Risto Atanasov Geometric Two-Dimensional Duality Groups ... weak exhaustiveness and (strong uniform) continuity Vitalij A. Chatyrko Some topological properties of unions of Vitali sets Kocev Darko ...
In this paper, we obtain a new characterization of Hilbert spaces by means of polynomial mappings... more In this paper, we obtain a new characterization of Hilbert spaces by means of polynomial mappings, extending the linear result of Kwapie´n.
La notion des opérateurs p−lattice sommants aété introduite etétudiée par Yannovskii dans [10] po... more La notion des opérateurs p−lattice sommants aété introduite etétudiée par Yannovskii dans [10] pour p = 1 et généralisée par Nielsen et Szulga dans [7] et [8]. Dans ce papier, onétudie les opérateurs sous-linéaires p−lattice sommants. On essaie de caractériser ces opérateurs comme dans le cas linéaire. On conjecture que certaines propriétés (qui sont liées les unes aux autres) valables dans le cas linéaire seront aussi valables dans le cas sous linéaire. Si l'une des conjectures est vraie, on pourra montrer que le théorème de Grothendieck pour le cas sous linéaire ne sera pas valide. 2000 Mathematics Subject Classification. 46B42, 46B40, 47B460, 47B65.
Rendiconti del Circolo Matematico di Palermo, 2011
In this paper we introduce and study a new class containing the class of absolutely summing multi... more In this paper we introduce and study a new class containing the class of absolutely summing multilinear mappings, which we call absolutely (p;q 1,…,q m ;r)-summing multilinear mappings. We investigate some interesting properties concerning the absolutely (p;q 1,…,q m ;r)-summing m-linear mappings defined on Banach spaces. In particular, we prove a kind of Pietsch’s Domination Theorem and a multilinear version of the Factorization Theorem.
Annals of Functional Analysis, 2011
In this paper we consider the ideal of Cohen p-nuclear multilinear mappings, which is a natural m... more In this paper we consider the ideal of Cohen p-nuclear multilinear mappings, which is a natural multilinear extension of the ideal of p-nuclear linear operators. The space of Cohen p-nuclear m-linear mappings is characterized by means of a suitable tensor norm up to an isometric isomorphism.
Further Progress in Analysis - Proceedings of the 6th International ISAAC Congress, 2009
Colloquium Mathematicum, 2010
Linear and Multilinear Algebra, 2013
ABSTRACT We introduce the new ideal of strongly[Inline formula]-continuous linear operators in or... more ABSTRACT We introduce the new ideal of strongly[Inline formula]-continuous linear operators in order to study the adjoints of the [Inline formula]-absolutely continuous linear operators. Starting from this ideal we build a new multi-ideal by using the composition method. We prove the corresponding Pietsch domination theorem and we present a representation of this multi-ideal by a tensor norm. A factorization theorem characterizing the corresponding multi-ideal – which is also new for the linear case – is given. When applied to the case of the Cohen strongly [Inline formula]-summing operators, this result gives also a new factorization theorem.
Journal of Mathematical Analysis and Applications, 2007
In this paper, we introduce and study a new concept of summability in the category of multilinear... more In this paper, we introduce and study a new concept of summability in the category of multilinear operators, which is the Cohen strongly p-summing multilinear operators. We prove a natural analog of the Pietsch domination theorem and we compare the notion of p-dominated multilinear operators with this class by generalizing a theorem of Bu-Cohen.
Journal of Mathematical Analysis and Applications, 2013
ABSTRACT In this paper, we obtain a new characterization of Hilbert spaces by means of polynomial... more ABSTRACT In this paper, we obtain a new characterization of Hilbert spaces by means of polynomial mappings, extending the linear result of Kwapień. Keywords46G25-47H60 MSC2000Homogeneous polynomials-Cohen stronglyp-summing-absolutelyp-summing- p-dominated-stronglyp-summing-Pietsch domination theorem
atlas-conferences.com
... Beti Andonovic Coherent Proximate Nets and Strong Shape of Metric Compacta Risto Atanasov Geo... more ... Beti Andonovic Coherent Proximate Nets and Strong Shape of Metric Compacta Risto Atanasov Geometric Two-Dimensional Duality Groups ... weak exhaustiveness and (strong uniform) continuity Vitalij A. Chatyrko Some topological properties of unions of Vitali sets Kocev Darko ...