Exactness of some (0,1)-forms in Hilbert spaces of infinite dimension


  • Abdallah Talhaoui

    1. Laboratoire Paul Painlevé CNRS UMR 8524,UFR de Mathématiques, Université des Sciences et Technologies de Lille,F–59665 Villeneuve d'Ascq Cedex, France, Phone: +213 (0)7 77 89 69 30, Fax: +213 (0)41 58 20 66
    2. Département de Mathématiques & Informatique,E.N.S.E.T. d'Oran, BP 1523 El Menaouer 31000, Oran, Algérie
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We study the local exactness of the equation image operator in the Hilbert space l2 for a particular class of (0, 1)-forms ω of the type equation image, z = (zi) in l2. We suppose that each function ωi of class C in the closure of the unit ball of l2, of the form equation image, where equation image is a partition of equation image (card Ik < +∞) and zk is the projection of z on equation image. We obtain a positive result (Theorem 1.1) when the sequence (card Ik) is bounded. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim