Browsing by Author "MANSOUR Abdelouahab"

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    EXTENDED SPECTRUM, NUMERICAL RANGE OF OPERATORS AND ALUTHGE TRANSFORMATION AND INTERACTIONS
    (University Of Eloued جامعة الوادي, 2020-02-23) GUEMOULA Asma; MANSOUR Abdelouahab; HECHIFA Abderazak
    around two themes : a transformation of B (H) introduced by Aluthge, the first part is the subject of the study of the transformation of Aluthge which has had a significant impact in recent years in operator theory . Optimal results on the stability of a certain number of operator classes, such as the class of partial isometrics and the classes associated with the asymptotic behavior of an operator, are provided. We also study the evolution of operator invariants, such as the minimum polynomial, the minimum function, the ascent and the descent, under the action of the transformation ; we compare more precisely the sequences of nuclei and images relating to the iterates of an operator and its Aluthge transform, and the second part will be devoted to the study of numerical range and a fairly recent spectral concept, called the extended spectrum operators...
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    EXTENDED SPECTRUM, NUMERICAL RANGE OF OPERATORS AND ALUTHGE TRANSFORMATION AND INTERACTIONS
    (University Of Eloued جامعة الوادي, 2020-02-23) GUEMOULA Asma; MANSOUR Abdelouahab; HECHIFA Abderazak
    The aim of this paper is to show the existence, uniqueness, and asymptotic behavior of time-dependent solutions. Also in- vestigated is the existence of positive maximal and minimal so- lutions of the corresponding quasilinear elliptic system. The el- liptic operators in both systems are allowed to be degenerate in the sense that the density-dependent di¤usion coe¢ cients Di (ui) may have the property Di (0) = 0 for some or all i = 1;...;N, and the boundary condition is ui = 0. Using the method of up- per and lower solutions, we show that a unique global classical time-dependent solution exists and converges to the maximal so- lution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution.