On Some New Classes Of Lipschitz Summing Operators

Résumé: The context of this thesis falls within the framework of functional analysis and more precisely in nonlinear geometry. The ideas of this work were inspired from the article of J.D. Farmer and W.B. Jonhnson entitled "Lipschitz p-summing operators" and from the paper of R. Khalil and W. Deeb entitled " -summing operators in Banach spaces"; also that of K. Saadi entitled "On the composition ideals of Lipschitz mappings". In the rst part, our contribution consisted in the following idea: from a linear -summing operator between Banach spaces, where is a modulus function, we have introduced the notion of Lipschitz -summing operator between metric spaces giving a nonlinear version of Pietsch domination theorem for these operators and some properties concerning this class. In the second part, from the notion of Lipschitz strictly p-summing operators we have given new characterizations of this class, where we have adapted this de nition for constructing other class of Lipschitz mappings which are called M-strictly lipschiz p-summing operators and strictly Lipschitz p-nuclear operators and strictly Lipschitz (p; r; s)-summing operators, in addition to all that, we obtained also some interesting results for these new classes. In the end of this thesis, we present a short section collecting some interesting open problems.

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