Doctoral Dissertations

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Browsing Doctoral Dissertations by Author "ASMA HAMMOU"

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    Nuclear operators and its applications "Les opérateurs nucléaires et leurs applications"
    (University of M'Sila, 2024-04-27) ASMA HAMMOU
    In the present study, our primary main is extend operator ideal theory to multilinear operators and polynomials. In this context, we direct our attention towards the study of two distinct concepts to p-nuclear operators. The first study involves an extension of the notion of weakly p-nuclear operators, which was introduced by J.M. Kim, in (J. Korean Math. Soc 56 (2019), 225-237), to encompass multilinear operators and polynomials. We show that this class forms a Banach multi-ideal (respectively, polynomials), In the quest to look for a class of operators that represent bounded linear functionals on the space of weakly p-nuclear multilinear operators (respectively, polynomials) led us to the introduction of the class of quasi Cohen p-nuclear multilinear operators (respectively, polynomials). We show that such operators realise a Pietsch domination theorem. Moreover, we prove that, under the usual conditions, there exists an isometric isomorphism between the dual of the space of weakly p-nuclear multilinear operators (respectively, polynomials) and the space of quasi Cohen p- nuclear multilinear operators (respectively, polynomials). The second study is the extension of the concept of Cohen p-nuclear operators introduced by J. S. Cohen in (Math. Ann. 201(1973) 177-201) to polynomials between Banach lattices, we show that a polynomial is positive Cohen p-nuclear if, and only if, its associated symmetric multilinear operator is positive Cohen p-nuclear. Additionally, the study defines positive Cohen p-nuclear polynomials as a combination of positive Cohen strongly p-summing polynomials and positive absolutely p-summing linear operators, and shedding light on their relationship with other classes.