Geomerty of Müntz spaces and weighted composition operators

L'objet de cette thèse de doctorat est d'étudier quelques aspects géométriques des espaces de Müntz (M'A et M~) dans C([O,l]) et LP([O,l]), 1 ::; p < 00. Ce travail comporte quatre chapitres. Le premier chapitre est consacré aux préliminaires. Dans le deuxième chapitre, nous démontrerons plusieurs propriétés élémentaires des espaces de Müntz, ces propriétés expliquent la nature géométrique de ces espaces. On s'intéresse aussi à une nouvelle généralisation des espaces de Müntz en considérant les polynômes de Müntz à coefficients dans un Banach quelconque X. Dans le troisième chapitre, On construit un espace de Müntz n'ayant pas de complément dans LI ([0,1]). Comme application de ce travail, on retrouve certains résultats qui ont était récemment obtenus dans le livre de Vladimir I.Gurariy et Wolfgang Lusky, mais avec une méthode complètement différente. On donne aussi une base de Schauder explicite équivalente à la base canonique dans gl pour certains espaces de Müntz MX, avec A une suite non lacunaire. Dans une deuxième partie de ce chapitre, on étudie le cas LP([O, 1]), 1 ::; p < 00, nous verrons que certains phénomènes passent du cas p = 1 au cas p quelconque. Enfin, dans un quatrième chapitre on étudie les opérateurs de composition à poids sur les espaces de Müntz classiques. Notre résultat principal donne une estimation précise de la norme essentielle de cet opérateur agissant sur M'A en termes de valeur de cp et '!/J. Dans la deuxième partie de ce chapitre on étudie les opérateurs de composition à poids, définis sur les espaces de Müntz MX dans LI.The main subject of this PHD thesis is the study of sorne geometric aspects of Müntz spaces (M'A and M~) in C([O, 1]) and LP([O, 1]),1 ::; p < 00. This work is composed offour chapters. The first chapter is devoted to preliminary. ln the second chapter, we prove sever al basic properties of Müntz spaces, these properties explain the geometric nature of these spaces. There is also a new generalization of Müntz spaces by considering the Müntz polynomials with coefficient in any Banach space X. The aim of the third one is to construct a Müntz space having no complement in LI ([0,1]). As an application of this work, we obtain sorne results that were recently obtained in the monograph of Vladimir I. Gurariy and Wolfgang Lusky, but with a method completely different. We also provide an explicit Schauder basis equivalent to the canonical base in gl for sorne Müntz spaces MX, with A not lacunary. ln a second part of this chapter, we study the case LP([O, 1]), 1 ::; p < 00, we will see that sorne phenomena still true in the case 1 < p < 00. Finally, in the fourth chapter, we discuss the problem of compactness for weighted composition operators T'ljJoC<p, defined on a Müntz space M'A. We compute the essential norm of such operators in terms of the value of r.p and '!/J. As a corollary, we obtain the exact values of essential norms of composition and multiplication operators. ln the second part of this chapter we study the weighted composition operators T'ljJoC<p, defined on a Müntz space MX in LI. TITRE DE LATHESE EN ANGLAIS: Transcrire en toutes lettres les symboles s'''pPiéc'''la:rnu;Vx-------------- Geometry o

Essential Norms of Weighted Composition Operators on L^1 Müntz Spaces

This paper discusses the problem of boundedness and compactness for weighted composition operators defined on a Müntz subspace of L^1([0,1]). We compute the essential norm of such operators when the symbol ϕ of the composition operator satisfies a special condition (condition (β)). As a corollary, we obtain the exact values of essential norms of composition and multiplication operators. This completes the corresponding results of the first named author in the framework of Müntz subspaces of C([0, 1]). 2010 Mathematics Subject Classification: 47B33, 47B38

Géométrie des espaces de Müntz et opérateurs de composition à poids

L'objet de cette thèse de doctorat est d'étudier quelques aspects géométriques des espaces de Müntz (M'A et M~) dans C([O,l]) et LP([O,l]), 1 ::; p < 00. Ce travail comporte quatre chapitres. Le premier chapitre est consacré aux préliminaires. Dans le deuxième chapitre, nous démontrerons plusieurs propriétés élémentaires des espaces de Müntz, ces propriétés expliquent la nature géométrique de ces espaces. On s'intéresse aussi à une nouvelle généralisation des espaces de Müntz en considérant les polynômes de Müntz à coefficients dans un Banach quelconque X. Dans le troisième chapitre, On construit un espace de Müntz n'ayant pas de complément dans LI ([0,1]). Comme application de ce travail, on retrouve certains résultats qui ont était récemment obtenus dans le livre de Vladimir I.Gurariy et Wolfgang Lusky, mais avec une méthode complètement différente. On donne aussi une base de Schauder explicite équivalente à la base canonique dans gl pour certains espaces de Müntz MX, avec A une suite non lacunaire. Dans une deuxième partie de ce chapitre, on étudie le cas LP([O, 1]), 1 ::; p < 00, nous verrons que certains phénomènes passent du cas p = 1 au cas p quelconque. Enfin, dans un quatrième chapitre on étudie les opérateurs de composition à poids sur les espaces de Müntz classiques. Notre résultat principal donne une estimation précise de la norme essentielle de cet opérateur agissant sur M'A en termes de valeur de cp et '!/J. Dans la deuxième partie de ce chapitre on étudie les opérateurs de composition à poids, définis sur les espaces de Müntz MX dans LI.The main subject of this PHD thesis is the study of sorne geometric aspects of Müntz spaces (M'A and M~) in C([O, 1]) and LP([O, 1]),1 ::; p < 00. This work is composed offour chapters. The first chapter is devoted to preliminary. ln the second chapter, we prove sever al basic properties of Müntz spaces, these properties explain the geometric nature of these spaces. There is also a new generalization of Müntz spaces by considering the Müntz polynomials with coefficient in any Banach space X. The aim of the third one is to construct a Müntz space having no complement in LI ([0,1]). As an application of this work, we obtain sorne results that were recently obtained in the monograph of Vladimir I. Gurariy and Wolfgang Lusky, but with a method completely different. We also provide an explicit Schauder basis equivalent to the canonical base in gl for sorne Müntz spaces MX, with A not lacunary. ln a second part of this chapter, we study the case LP([O, 1]), 1 ::; p < 00, we will see that sorne phenomena still true in the case 1 < p < 00. Finally, in the fourth chapter, we discuss the problem of compactness for weighted composition operators T'ljJoC<p, defined on a Müntz space M'A. We compute the essential norm of such operators in terms of the value of r.p and '!/J. As a corollary, we obtain the exact values of essential norms of composition and multiplication operators. ln the second part of this chapter we study the weighted composition operators T'ljJoC<p, defined on a Müntz space MX in LI. TITRE DE LATHESE EN ANGLAIS: Transcrire en toutes lettres les symboles s'''pPiéc'''la:rnu;Vx- Geometry ofLILLE1-Bib. Electronique (590099901) / SudocSudocFranceF

Géométrie des espaces de Müntz et opérateurs de composition à poids

L'objet de cette thèse de doctorat est d'étudier quelques aspects géométriques des espaces de Müntz (M'A et M~) dans C([O,l]) et LP([O,l]), 1 ::; p < 00. Ce travail comporte quatre chapitres. Le premier chapitre est consacré aux préliminaires. Dans le deuxième chapitre, nous démontrerons plusieurs propriétés élémentaires des espaces de Müntz, ces propriétés expliquent la nature géométrique de ces espaces. On s'intéresse aussi à une nouvelle généralisation des espaces de Müntz en considérant les polynômes de Müntz à coefficients dans un Banach quelconque X. Dans le troisième chapitre, On construit un espace de Müntz n'ayant pas de complément dans LI ([0,1]). Comme application de ce travail, on retrouve certains résultats qui ont était récemment obtenus dans le livre de Vladimir I.Gurariy et Wolfgang Lusky, mais avec une méthode complètement différente. On donne aussi une base de Schauder explicite équivalente à la base canonique dans gl pour certains espaces de Müntz MX, avec A une suite non lacunaire. Dans une deuxième partie de ce chapitre, on étudie le cas LP([O, 1]), 1 ::; p < 00, nous verrons que certains phénomènes passent du cas p = 1 au cas p quelconque. Enfin, dans un quatrième chapitre on étudie les opérateurs de composition à poids sur les espaces de Müntz classiques. Notre résultat principal donne une estimation précise de la norme essentielle de cet opérateur agissant sur M'A en termes de valeur de cp et '!/J. Dans la deuxième partie de ce chapitre on étudie les opérateurs de composition à poids, définis sur les espaces de Müntz MX dans LI.The main subject of this PHD thesis is the study of sorne geometric aspects of Müntz spaces (M'A and M~) in C([O, 1]) and LP([O, 1]),1 ::; p < 00. This work is composed offour chapters. The first chapter is devoted to preliminary. ln the second chapter, we prove sever al basic properties of Müntz spaces, these properties explain the geometric nature of these spaces. There is also a new generalization of Müntz spaces by considering the Müntz polynomials with coefficient in any Banach space X. The aim of the third one is to construct a Müntz space having no complement in LI ([0,1]). As an application of this work, we obtain sorne results that were recently obtained in the monograph of Vladimir I. Gurariy and Wolfgang Lusky, but with a method completely different. We also provide an explicit Schauder basis equivalent to the canonical base in gl for sorne Müntz spaces MX, with A not lacunary. ln a second part of this chapter, we study the case LP([O, 1]), 1 ::; p < 00, we will see that sorne phenomena still true in the case 1 < p < 00. Finally, in the fourth chapter, we discuss the problem of compactness for weighted composition operators T'ljJoC<p, defined on a Müntz space M'A. We compute the essential norm of such operators in terms of the value of r.p and '!/J. As a corollary, we obtain the exact values of essential norms of composition and multiplication operators. ln the second part of this chapter we study the weighted composition operators T'ljJoC<p, defined on a Müntz space MX in LI. TITRE DE LATHESE EN ANGLAIS: Transcrire en toutes lettres les symboles s'''pPiéc'''la:rnu;Vx- Geometry ofLILLE1-Bib. Electronique (590099901) / SudocSudocFranceF

Essential norms of Volterra and Cesàro operators on Müntz spaces

We study the properties of the Volterra and Cesàro operators viewed on the L 1-Müntz space with range in the space of continuous functions. These operators are neither compact nor weakly compact. We estimate how far from being (weakly) compact they are by computing their (generalized) essential norm. It turns out that this latter does not depend on Λ and is equal to 1/2

Essential norm of Cesàro operators on L p and Cesàro spaces

In this paper, we consider the Cesàro-mean operator Γ acting on some Banach spaces of measurable functions on (0, 1), as well as its discrete version on some sequences spaces. We compute the essential norm of this operator on L p ([0, 1]), for p ∈ (1, +∞] and show that its value is the same as its norm, namely p/(p − 1). The result also holds in the discrete case. On Cesàro spaces, the essential norm of Γ turns out to be equal to 1. Lastly, we introduce the Müntz-Cesàro spaces and study some of their geometrical properties. In this framework, we also compute the essential norm of the Cesàro and multiplication operators restricted to those Müntz-Cesàro spaces

Role of Magnetite Nanoparticles Size and Concentration on Hyperthermia under Various Field Frequencies and Strengths

Magnetite (Fe3O4) nanoparticles were synthesized using the chemical coprecipitation method. Several nanoparticle samples were synthesized by varying the concentration of iron salt precursors in the solution for the synthesis. Two batches of nanoparticles with average sizes of 10.2 nm and 12.2 nm with nearly similar particle-size distributions were investigated. The average particle sizes were determined from the XRD patterns and TEM images. For each batch, several samples with different particle concentrations were prepared. Morphological analysis of the samples was performed using TEM. The phase and structure of the particles of each batch were studied using XRD, selected area electron diffraction (SAED), Raman and XPS spectroscopy. Magnetic hysteresis loops were obtained using a Lakeshore vibrating sample magnetometer (VSM) at room temperature. In the two batches, the particles were found to be of the same pure crystalline phase of magnetite. The effects of particle size, size distribution, and concentration on the magnetic properties and magneto thermic efficiency were investigated. Heating profiles, under an alternating magnetic field, were obtained for the two batches of nanoparticles with frequencies 765.85, 634.45, 491.10, 390.25, 349.20, 306.65, and 166.00 kHz and field amplitudes of 100, 200, 250, 300 and 350 G. The specific absorption rate (SAR) values for the particles of size 12.2 nm are higher than those for the particles of size 10.2 nm at all concentrations and field parameters. SAR decreases with the increase of particle concentration. SAR obtained for all the particle concentrations of the two batches increases almost linearly with the field frequency (at fixed field strength) and nonlinearly with the field amplitude (at fixed field frequency). SAR value obtained for magnetite nanoparticles with the highest magnetization is 145.84 W/g at 765.85 kHz and 350 G, whereas the SAR value of the particles with the least magnetization is 81.67 W/g at the same field and frequency

Role of Magnetite Nanoparticles Size and Concentration on Hyperthermia under Various Field Frequencies and Strengths

Magnetite (Fe3O4) nanoparticles were synthesized using the chemical coprecipitation method. Several nanoparticle samples were synthesized by varying the concentration of iron salt precursors in the solution for the synthesis. Two batches of nanoparticles with average sizes of 10.2 nm and 12.2 nm with nearly similar particle-size distributions were investigated. The average particle sizes were determined from the XRD patterns and TEM images. For each batch, several samples with different particle concentrations were prepared. Morphological analysis of the samples was performed using TEM. The phase and structure of the particles of each batch were studied using XRD, selected area electron diffraction (SAED), Raman and XPS spectroscopy. Magnetic hysteresis loops were obtained using a Lakeshore vibrating sample magnetometer (VSM) at room temperature. In the two batches, the particles were found to be of the same pure crystalline phase of magnetite. The effects of particle size, size distribution, and concentration on the magnetic properties and magneto thermic efficiency were investigated. Heating profiles, under an alternating magnetic field, were obtained for the two batches of nanoparticles with frequencies 765.85, 634.45, 491.10, 390.25, 349.20, 306.65, and 166.00 kHz and field amplitudes of 100, 200, 250, 300 and 350 G. The specific absorption rate (SAR) values for the particles of size 12.2 nm are higher than those for the particles of size 10.2 nm at all concentrations and field parameters. SAR decreases with the increase of particle concentration. SAR obtained for all the particle concentrations of the two batches increases almost linearly with the field frequency (at fixed field strength) and nonlinearly with the field amplitude (at fixed field frequency). SAR value obtained for magnetite nanoparticles with the highest magnetization is 145.84 W/g at 765.85 kHz and 350 G, whereas the SAR value of the particles with the least magnetization is 81.67 W/g at the same field and frequency